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Math Calculus Calculus: Early Transcendentals (2nd Edition)

Gravitational force The magnitude of the gravitational force between two objects of mass M and m is given by F ( x ) = − G M m x 2 , where x is the distance between the centers of mass of the objects and G = 6.7 × 10 −11 N·m 2 /kg 2 is the gravitational constant (N stands for newton, the unit of force: the negative sign indicates an attractive force). a. Find the instantaneous rate of change of the force with respect to the distance between the objects. b. For two identical objects of mass M = m = 0.1 kg, what is the instantaneous rate of change of the force at a separation of x = 0.01 m? c. Does the instantaneous rate of change of the force increase or decrease with the separation? Explain.

Gravitational force The magnitude of the gravitational force between two objects of mass M and m is given by F ( x ) = − G M m x 2 , where x is the distance between the centers of mass of the objects and G = 6.7 × 10 −11 N·m 2 /kg 2 is the gravitational constant (N stands for newton, the unit of force: the negative sign indicates an attractive force). a. Find the instantaneous rate of change of the force with respect to the distance between the objects. b. For two identical objects of mass M = m = 0.1 kg, what is the instantaneous rate of change of the force at a separation of x = 0.01 m? c. Does the instantaneous rate of change of the force increase or decrease with the separation? Explain.

Calculus: Early Transcendentals (2nd Edition)

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 3.4, Problem 82E

Gravitational force The magnitude of the gravitational force between two objects of mass M and m is given by F ( x ) = − G M m x 2 , where x is the distance between the centers of mass of the objects and G = 6.7 × 10⁻¹¹ N·m²/kg² is the gravitational constant (N stands for newton, the unit of force: the negative sign indicates an attractive force).

a. Find the instantaneous rate of change of the force with respect to the distance between the objects.
b. For two identical objects of mass M = m = 0.1 kg, what is the instantaneous rate of change of the force at a separation of x = 0.01 m?
c. Does the instantaneous rate of change of the force increase or decrease with the separation? Explain.

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Chapter 3.4, Problem 81E

Chapter 3.4, Problem 83E

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Chapter 3 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 3.1 - Use definition (1) (p. 127) for the slope of a...Ch. 3.1 - Explain why the slope of a secant line can be...Ch. 3.1 - Explain why the slope of the tangent line can be...Ch. 3.1 - Prob. 4E Ch. 3.1 - Given a function f and a point a in its domain,...Ch. 3.1 - Explain the relationships among the slope of a...Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Equations of tangent lines by definition (1) a....

Ch. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Prob. 12E Ch. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Prob. 26E Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - A derivative formula a. Use the definition of the...Ch. 3.1 - A derivative formula a. Use the definition of the...Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Explain why or why not Determine whether the...Ch. 3.1 - Slope of a line Consider the line f(x) = mx + b,...Ch. 3.1 - Calculating derivatives a. For the following...Ch. 3.1 - Calculating derivatives a. For the following...Ch. 3.1 - Calculating derivatives a. For the following...Ch. 3.1 - Calculating derivatives a. For the following...Ch. 3.1 - Analyzing slopes Use the points A, B, C, D, and E...Ch. 3.1 - Analyzing slopes Use the points A, B, C, D, and E...Ch. 3.1 - Power and energy Energy is the capacity to do...Ch. 3.1 - Population of Las Vegas Let p(t) represent the...Ch. 3.1 - Find the function The following limits represent...Ch. 3.1 - Find the function The following limits represent...Ch. 3.1 - Find the function The following limits represent...Ch. 3.1 - Find the function The following limits represent...Ch. 3.1 - Prob. 61E Ch. 3.1 - Looking ahead: Derivative of xn Use the definition...Ch. 3.1 - Prob. 63E Ch. 3.1 - Approximating derivatives Assuming the limit...Ch. 3.1 - Approximating derivatives Assuming the limit...Ch. 3.1 - Prob. 66E Ch. 3.1 - Approximating derivatives Assuming the limit...Ch. 3.2 - Explain why f(x) could be positive or negative at...Ch. 3.2 - Prob. 2E Ch. 3.2 - If f is differentiable at a, must f be continuous...Ch. 3.2 - If f is continuous at a, must f be differentiable...Ch. 3.2 - Derivatives from graphs Use the graph of f to...Ch. 3.2 - Derivatives from graphs Use the graph of f to...Ch. 3.2 - Matching functions with derivatives Match graphs...Ch. 3.2 - Matching derivatives with functions Match graphs...Ch. 3.2 - Matching functions with derivatives Match the...Ch. 3.2 - Sketching derivatives Reproduce the graph of f and...Ch. 3.2 - Sketching derivatives Reproduce the graph of f and...Ch. 3.2 - Sketching derivatives Reproduce the graph of f and...Ch. 3.2 - Graphing the derivative with asymptotes Sketch a...Ch. 3.2 - Graphing the derivative with asymptotes Sketch a...Ch. 3.2 - Where is the function continuous? Differentiable?...Ch. 3.2 - Where is the function continuous? Differentiable?...Ch. 3.2 - Explain why or why not Determine whether the...Ch. 3.2 - Prob. 18E Ch. 3.2 - Finding f from f Sketch the graph of f(x) = x....Ch. 3.2 - Prob. 20E Ch. 3.2 - Normal lines A line perpendicular to another line...Ch. 3.2 - Normal lines A line perpendicular to another line...Ch. 3.2 - Normal lines A line perpendicular to another line...Ch. 3.2 - Prob. 24E Ch. 3.2 - Aiming a tangent line Given the function f and the...Ch. 3.2 - Aiming a tangent line Given the function f and the...Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Voltage on a capacitor A capacitor is a device in...Ch. 3.2 - Logistic growth A common model for population...Ch. 3.2 - One-sided derivatives The right-sided and...Ch. 3.2 - One-sided derivatives The right-sided and...Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Vertical tangent lines If a function f is...Ch. 3.2 - Continuity is necessary for differentiability a....Ch. 3.3 - Assume the derivatives of f and g exist in...Ch. 3.3 - Assume the derivatives of f and g exist in...Ch. 3.3 - Assume the derivatives of f and g exist in...Ch. 3.3 - Prob. 4E Ch. 3.3 - Assume the derivatives of f and g exist in...Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Derivatives of power and constant functions Find...Ch. 3.3 - Prob. 9E Ch. 3.3 - Derivatives of power and constant functions Find...Ch. 3.3 - Derivatives of power and constant functions Find...Ch. 3.3 - Prob. 12E Ch. 3.3 - Derivatives of constant multiples of functions...Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Derivatives of constant multiples of functions...Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Derivatives of the sum of functions Find the...Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Equations of tangent lines a. Find an equation of...Ch. 3.3 - Equations of tangent lines a. Find an equation of...Ch. 3.3 - Equations of tangent lines a. Find an equation of...Ch. 3.3 - Equations of tangent lines a. Find an equation of...Ch. 3.3 - Finding slope locations Let f(x) = x3 6x + 5. a....Ch. 3.3 - Finding slope locations Let f(t) = t3 27t + 5. a....Ch. 3.3 - Finding slope locations Let f(x) = 2x3 3x2 12x +...Ch. 3.3 - Finding slope locations Let f(x) = 2ex 6x. a....Ch. 3.3 - Finding slope locations Let f(x)=4xx. a. Find all...Ch. 3.3 - Higher-order derivatives Find f(x), f(x), and f(x)...Ch. 3.3 - Higher-order derivatives Find f(x), f(x), and f(x)...Ch. 3.3 - Higher-order derivatives Find f(x), f(x), and f(x)...Ch. 3.3 - Higher-order derivatives Find f(x), f(x), and f(x)...Ch. 3.3 - Higher-order derivatives Find f(x), f(x), and f(x)...Ch. 3.3 - Explain why or why not Determine whether the...Ch. 3.3 - Tangent lines Suppose f(3) = 1 and f(3) = 4. Let...Ch. 3.3 - Derivatives from tangent lines Suppose the line...Ch. 3.3 - Tangent line Find the equation of the line tangent...Ch. 3.3 - Tangent line given Determine the constants b and c...Ch. 3.3 - Derivatives from a graph Let F = f + g and G = 3f ...Ch. 3.3 - Derivatives from a graph Let F = f + g and G = 3f ...Ch. 3.3 - Derivatives from a graph Let F = f + g and G = 3f ...Ch. 3.3 - Derivatives from a graph Let F = f + g and G = 3f ...Ch. 3.3 - Derivatives from a table Use the table to find the...Ch. 3.3 - Derivatives from a table Use the table to find the...Ch. 3.3 - Derivatives from a table Use the table to find the...Ch. 3.3 - Derivatives from limits The following limits...Ch. 3.3 - Derivatives from limits The following limits...Ch. 3.3 - Derivatives from limits The following limits...Ch. 3.3 - Prob. 64E Ch. 3.3 - Prob. 65E Ch. 3.3 - Calculator limits Use a calculator to approximate...Ch. 3.3 - Prob. 67E Ch. 3.3 - Prob. 68E Ch. 3.3 - Prob. 69E Ch. 3.3 - Projectile trajectory The position of a small...Ch. 3.3 - Prob. 71E Ch. 3.3 - Cell growth When observations begin at t = 0, a...Ch. 3.3 - City urbanization City planners model the size of...Ch. 3.3 - Constant Rule proof For the constant function f(x)...Ch. 3.3 - Prob. 75E Ch. 3.3 - Looking ahead: Power Rule for negative integers...Ch. 3.3 - Prob. 77E Ch. 3.3 - Computing the derivative of f(x) = ex a. Use the...Ch. 3.3 - Prob. 79E Ch. 3.3 - Computing the derivative of f(x) = x2ex a. Use the...Ch. 3.4 - How do you find the derivative of the product of...Ch. 3.4 - How do you find the derivative of the quotient of...Ch. 3.4 - Prob. 3E Ch. 3.4 - Show two ways to differentiate f(x) = 1/x10.Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 24E Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Prob. 30E Ch. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Equations of tangent lines a. Find an equation of...Ch. 3.4 - Equations of tangent lines a. Find an equation of...Ch. 3.4 - Equations of tangent lines a. Find an equation of...Ch. 3.4 - Equations of tangent lines a. Find an equation of...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - Population growth Consider the following...Ch. 3.4 - Prob. 52E Ch. 3.4 - Antibiotic decay The half-life of an antibiotic in...Ch. 3.4 - Bank account A 200 investment in a savings account...Ch. 3.4 - Finding slope locations Let f(x) = xe2x. a. Find...Ch. 3.4 - Prob. 56E Ch. 3.4 - Combining rules Compute the derivative of the...Ch. 3.4 - Combining rules Compute the derivative of the...Ch. 3.4 - Combining rules Compute the derivative of the...Ch. 3.4 - Combining rules Compute the derivative of the...Ch. 3.4 - Prob. 61E Ch. 3.4 - Higher-order derivatives Find f(x), f(x), and...Ch. 3.4 - Prob. 63E Ch. 3.4 - First and second derivatives Find f(x) and f(x)....Ch. 3.4 - First and second derivatives Find f(x) and f(x)....Ch. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Prob. 68E Ch. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Tangent lines Suppose f(2) = 2 and f(2) = 3. Let...Ch. 3.4 - The Witch of Agnesi The graph of y=a3x2+a2, where...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Derivatives from tangent lines Suppose the line...Ch. 3.4 - Electrostatic force The magnitude of the...Ch. 3.4 - Gravitational force The magnitude of the...Ch. 3.4 - Prob. 83E Ch. 3.4 - Prob. 84E Ch. 3.4 - Prob. 85E Ch. 3.4 - Proof of the Quotient Rule Let F = f/g be the...Ch. 3.4 - Product Rule for the second derivative Assuming...Ch. 3.4 - Prob. 88E Ch. 3.4 - Derivative of ekx for negative integers k Use the...Ch. 3.4 - Prob. 90E Ch. 3.4 - Product Rule for three functions Assume that f, g,...Ch. 3.4 - One of the Leibniz Rules One of several Leibniz...Ch. 3.5 - Why is it not possible to evaluate limx0sinxx by...Ch. 3.5 - How is limx0sinxx used in this section?Ch. 3.5 - Explain why the Quotient Rule is used to determine...Ch. 3.5 - How can you use the derivatives ddx(sinx)=cosx,...Ch. 3.5 - Let f(x) = sin x. What is the value of f()?Ch. 3.5 - Where does the graph of sin x have a horizontal...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 22E Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 26E Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Derivatives of other trigonometric functions...Ch. 3.5 - Derivatives of other trigonometric functions...Ch. 3.5 - Derivatives of other trigonometric functions...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Prob. 42E Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Second-order derivatives Find y for the following...Ch. 3.5 - Explain why or why not Determine whether the...Ch. 3.5 - Trigonometric limits Evaluate the following limits...Ch. 3.5 - Trigonometric limits Evaluate the following limits...Ch. 3.5 - Trigonometric limits Evaluate the following limits...Ch. 3.5 - Prob. 53E Ch. 3.5 - Prob. 54E Ch. 3.5 - Prob. 55E Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 59E Ch. 3.5 - Prob. 60E Ch. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Equations of tangent lines a. Find an equation of...Ch. 3.5 - Equations of tangent lines a. Find an equation of...Ch. 3.5 - Equations of tangent lines a. Find an equation of...Ch. 3.5 - Equations of tangent lines a. Find an equation of...Ch. 3.5 - Locations of tangent lines a. For what values of x...Ch. 3.5 - Locations of horizontal tangent lines For what...Ch. 3.5 - Matching Match the graphs of the functions in ad...Ch. 3.5 - Velocity of an oscillator An object oscillates...Ch. 3.5 - Prob. 70E Ch. 3.5 - A differential equation A differential equation is...Ch. 3.5 - Using identities Use the identity sin 2x = 2 sin x...Ch. 3.5 - Prob. 73E Ch. 3.5 - Prob. 74E Ch. 3.5 - Proof of ddx(cosx)=sinx Use the definition of the...Ch. 3.5 - Continuity of a piecewise function Let...Ch. 3.5 - Continuity of a piecewise function Let...Ch. 3.5 - Prob. 78E Ch. 3.5 - Prob. 79E Ch. 3.5 - Prob. 80E Ch. 3.5 - Prob. 81E Ch. 3.5 - Prob. 82E Ch. 3.5 - Prob. 83E Ch. 3.5 - Prob. 84E Ch. 3.5 - Prob. 85E Ch. 3.5 - Prob. 86E Ch. 3.6 - Explain the difference between the average rate of...Ch. 3.6 - Complete the following statement. If dydx is...Ch. 3.6 - Complete the following statement: If dydx is...Ch. 3.6 - What is the difference between the velocity and...Ch. 3.6 - Define the acceleration of an object moving in a...Ch. 3.6 - An object moving along a line has a constant...Ch. 3.6 - Prob. 7E Ch. 3.6 - Explain why a decreasing demand function has a...Ch. 3.6 - Highway travel A state patrol station is located...Ch. 3.6 - Airline travel The following figure shows the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - A stone thrown vertically on Mars Suppose a stone...Ch. 3.6 - Prob. 18E Ch. 3.6 - Population growth in Georgia The population of the...Ch. 3.6 - Consumer price index The U.S. consumer price index...Ch. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Demand and elasticity Based on sales data over the...Ch. 3.6 - Demand and elasticity The economic advisor of a...Ch. 3.6 - Prob. 27E Ch. 3.6 - Prob. 28E Ch. 3.6 - Explain why or why not Determine whether the...Ch. 3.6 - A feather dropped on the moon On the moon, a...Ch. 3.6 - Comparing velocities A stone is thrown vertically...Ch. 3.6 - Comparing velocities Two stones are thrown...Ch. 3.6 - Matching heights A stone is thrown from the edge...Ch. 3.6 - Velocity of a car The graph shows the position s =...Ch. 3.6 - Velocity from position The graph of s = f(t)...Ch. 3.6 - Fish length Assume the length L (in cm) of a...Ch. 3.6 - Average and marginal profit Let C(x) represent the...Ch. 3.6 - Average and marginal profit Let C(x) represent the...Ch. 3.6 - Average and marginal profit Let C(x) represent the...Ch. 3.6 - Average and marginal profit Let C(x) represent the...Ch. 3.6 - Prob. 41E Ch. 3.6 - Average and marginal production Economists use...Ch. 3.6 - Velocity of a marble The position (in meters) of a...Ch. 3.6 - Tree growth Let b represent the base diameter of a...Ch. 3.6 - Prob. 45E Ch. 3.6 - Diminishing returns A cost function of the form...Ch. 3.6 - Revenue function A store manager estimates that...Ch. 3.6 - Fuel economy Suppose you own a fuel-efficient...Ch. 3.6 - Spring oscillations A spring hangs from the...Ch. 3.6 - Pressure and altitude Earths atmospheric pressure...Ch. 3.6 - A race Jean and Juan run a one-lap race on a...Ch. 3.6 - Power and energy Power and energy are often used...Ch. 3.6 - Flow from a tank A cylindrical tank is full at...Ch. 3.6 - Prob. 54E Ch. 3.6 - Bungee jumper A woman attached to a bungee cord...Ch. 3.6 - Spring runoff The flow of a small stream is...Ch. 3.6 - Temperature distribution A thin copper rod, 4...Ch. 3.7 - Two equivalent forms of the Chain Rule for...Ch. 3.7 - Let h(x) = f(g(x)), where f and g are...Ch. 3.7 - Fill in the blanks. The derivative of f(g(x))...Ch. 3.7 - Prob. 4E Ch. 3.7 - Identify the inner and outer functions in the...Ch. 3.7 - Express Q(x) = cos4 (x2 + 1) as the composition of...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Prob. 10E Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Version 1 of the Chain Rule Use Version 1 of the...Ch. 3.7 - Prob. 18E Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 22E Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 31E Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 35E Ch. 3.7 - Prob. 36E Ch. 3.7 - Chain Rule using a table Let h(x)= f(g(x)) and...Ch. 3.7 - Prob. 38E Ch. 3.7 - Applying the Chain Rule Use the data in Tables 3.4...Ch. 3.7 - Chain Rule for powers Use the Chain Rule to find...Ch. 3.7 - Chain Rule for powers Use the Chain Rule to find...Ch. 3.7 - Prob. 43E Ch. 3.7 - Chain Rule for powers Use the Chain Rule to find...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Prob. 46E Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Prob. 50E Ch. 3.7 - Prob. 51E Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 65E Ch. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 67E Ch. 3.7 - Prob. 68E Ch. 3.7 - Explain why or why not Determine whether the...Ch. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Prob. 74E Ch. 3.7 - Square root derivatives Find the derivative of the...Ch. 3.7 - Prob. 76E Ch. 3.7 - Prob. 77E Ch. 3.7 - Tangent lines Determine equations of the lines...Ch. 3.7 - Tangent lines Assume f and g are differentiable on...Ch. 3.7 - Prob. 80E Ch. 3.7 - Tangent lines Find the equation of the line...Ch. 3.7 - Prob. 82E Ch. 3.7 - Composition containing sin x Suppose f is...Ch. 3.7 - Prob. 84E Ch. 3.7 - Prob. 85E Ch. 3.7 - Prob. 86E Ch. 3.7 - A damped oscillator The displacement of a mass on...Ch. 3.7 - Oscillator equation A mechanical oscillator (such...Ch. 3.7 - Prob. 89E Ch. 3.7 - Prob. 90E Ch. 3.7 - Prob. 91E Ch. 3.7 - Deriving trigonometric identities a. Differentiate...Ch. 3.7 - Prob. 93E Ch. 3.7 - Prob. 94E Ch. 3.7 - Prob. 95E Ch. 3.7 - Prob. 96E Ch. 3.7 - Prob. 97E Ch. 3.7 - Prob. 98E Ch. 3.7 - Prob. 99E Ch. 3.7 - Prob. 100E Ch. 3.7 - Prob. 101E Ch. 3.7 - Prob. 102E Ch. 3.7 - Prob. 103E Ch. 3.8 - For some equations, such as x2 + y2 = l or x y2 =...Ch. 3.8 - Explain the differences between computing the...Ch. 3.8 - Why are both the x-coordinate and the y-coordinate...Ch. 3.8 - In this section, for what values of n did we prove...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Prob. 27E Ch. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Second derivatives Find d2ydx2. 31. x + y2 = 1 Ch. 3.8 - Second derivatives Find d2ydx2. 32. 2x2 + y2 = 4 Ch. 3.8 - Second derivatives Find d2ydx2. 33. x + y = sin y Ch. 3.8 - Second derivatives Find d2ydx2. 34. x4 + y4 = 64 Ch. 3.8 - Second derivatives Find d2ydx2. 35. e2y + x = y Ch. 3.8 - Second derivatives Find d2ydx2 36. sin x + x2y =...Ch. 3.8 - Prob. 37E Ch. 3.8 - Prob. 38E Ch. 3.8 - Prob. 39E Ch. 3.8 - Prob. 40E Ch. 3.8 - Prob. 41E Ch. 3.8 - Prob. 42E Ch. 3.8 - Prob. 43E Ch. 3.8 - Prob. 44E Ch. 3.8 - Prob. 45E Ch. 3.8 - Prob. 46E Ch. 3.8 - Prob. 47E Ch. 3.8 - Prob. 48E Ch. 3.8 - Prob. 49E Ch. 3.8 - Prob. 50E Ch. 3.8 - Explain why or why not Determine whether the...Ch. 3.8 - Multiple tangent lines Complete the following...Ch. 3.8 - Multiple tangent lines Complete the following...Ch. 3.8 - Multiple tangent lines Complete the following...Ch. 3.8 - Witch of Agnesi Let y(x2 + 4) = 8 (see figure). a....Ch. 3.8 - Vertical tangent lines a. Determine the points at...Ch. 3.8 - Vertical tangent lines a. Determine the points...Ch. 3.8 - Tangent lines for ellipses Find the equations of...Ch. 3.8 - Tangent lines for ellipses Find the equations of...Ch. 3.8 - Prob. 60E Ch. 3.8 - Identifying functions from an equation The...Ch. 3.8 - Prob. 62E Ch. 3.8 - Prob. 63E Ch. 3.8 - Prob. 64E Ch. 3.8 - Normal lines A normal line at a point P on a curve...Ch. 3.8 - Normal lines A normal line at a point P on a curve...Ch. 3.8 - Prob. 67E Ch. 3.8 - Normal lines A normal line at a point P on a curve...Ch. 3.8 - Prob. 69E Ch. 3.8 - Normal lines A normal line at a point P on a curve...Ch. 3.8 - Prob. 71E Ch. 3.8 - Visualizing tangent and normal lines a. Determine...Ch. 3.8 - Visualizing tangent and normal lines a. Determine...Ch. 3.8 - Prob. 74E Ch. 3.8 - Cobb-Douglas production function The output of an...Ch. 3.8 - Surface area of a cone The lateral surface area of...Ch. 3.8 - Volume of a spherical cap Imagine slicing through...Ch. 3.8 - Volume of a torus The volume of a torus (doughnut...Ch. 3.8 - Orthogonal trajectories Two curves are orthogonal...Ch. 3.8 - Orthogonal trajectories Two curves are orthogonal...Ch. 3.8 - Orthogonal trajectories Two curves are orthogonal...Ch. 3.8 - Finding slope Find the slope of the curve...Ch. 3.8 - A challenging derivative Find dydx, where (x2 +...Ch. 3.8 - Prob. 84E Ch. 3.8 - A challenging derivative Find d2ydx2, where...Ch. 3.8 - Work carefully Proceed with caution when using...Ch. 3.8 - Work carefully Proceed with caution when using...Ch. 3.8 - Work carefully Proceed with caution when using...Ch. 3.8 - Work carefully Proceed with caution when using...Ch. 3.9 - Use x = ey to explain why ddx(lnx)=1x, for x 0.Ch. 3.9 - Prob. 2E Ch. 3.9 - Show that ddx(lnkx)=ddx(lnx), where x 0 and k is...Ch. 3.9 - State the derivative rule for the exponential...Ch. 3.9 - State the derivative rule for the logarithmic...Ch. 3.9 - Explain why bx = ex ln b Ch. 3.9 - Prob. 7E Ch. 3.9 - Prob. 8E Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Prob. 30E Ch. 3.9 - Exponential model The following table shows the...Ch. 3.9 - Magnitude of an earthquake The energy (in joules)...Ch. 3.9 - Diagnostic scanning Iodine-123 is a radioactive...Ch. 3.9 - Prob. 34E Ch. 3.9 - Prob. 35E Ch. 3.9 - Prob. 36E Ch. 3.9 - Prob. 37E Ch. 3.9 - General Power Rule Use the General Power Rule...Ch. 3.9 - Prob. 39E Ch. 3.9 - General Power Rule Use the General Power Rule...Ch. 3.9 - Prob. 41E Ch. 3.9 - Prob. 42E Ch. 3.9 - General Power Rule Use the General Power Rule...Ch. 3.9 - General Power Rule Use the General Power Rule...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Find an equation of the line tangent to y = xsin x...Ch. 3.9 - Determine whether the graph of y=xx has any...Ch. 3.9 - The graph of y = (x2)x has two horizontal tangent...Ch. 3.9 - The graph of y = xln x has one horizontal tangent...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Prob. 68E Ch. 3.9 - Prob. 69E Ch. 3.9 - Prob. 70E Ch. 3.9 - Higher-order derivatives Find the following...Ch. 3.9 - Higher-order derivatives Find the following...Ch. 3.9 - Higher-order derivatives Find the following...Ch. 3.9 - Derivatives by different methods Calculate the...Ch. 3.9 - Derivatives by different methods Calculate the...Ch. 3.9 - Prob. 76E Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Tangent lines Find the equation of the line...Ch. 3.9 - Horizontal tangents The graph of y = cos x ln...Ch. 3.9 - General logarithmic and exponential derivatives...Ch. 3.9 - General logarithmic and exponential derivatives...Ch. 3.9 - Prob. 87E Ch. 3.9 - Prob. 88E Ch. 3.9 - Prob. 89E Ch. 3.9 - General logarithmic and exponential derivatives...Ch. 3.9 - Prob. 91E Ch. 3.9 - Prob. 92E Ch. 3.9 - Logistic growth Scientists often use the logistic...Ch. 3.9 - Logistic growth Scientists often use the logistic...Ch. 3.9 - Prob. 95E Ch. 3.9 - Logistic growth Scientists often use the logistic...Ch. 3.9 - Savings plan Beginning at age 30, a self-employed...Ch. 3.9 - Tangency question It is easily verified that the...Ch. 3.9 - Tangency question It is easily verified that the...Ch. 3.9 - Triple intersection Graph the functions f(x) = x3,...Ch. 3.9 - Calculating limits exactly Use the definition of...Ch. 3.9 - Calculating limits exactly Use the definition of...Ch. 3.9 - Calculating limits exactly Use the definition of...Ch. 3.9 - Calculating limits exactly Use the definition of...Ch. 3.9 - Derivative of u(x)v(x) Use logarithmic...Ch. 3.9 - Tangent lines and exponentials. Assume b is given...Ch. 3.10 - State the derivative formulas for sin1 x, tan1 x,...Ch. 3.10 - What is the slope of the line tangent to the graph...Ch. 3.10 - What is the slope of the line tangent to the graph...Ch. 3.10 - How are the derivatives of sin1 x and cos1 x...Ch. 3.10 - Suppose f is a one-to-one function with f(2) = 8...Ch. 3.10 - Explain how to find (f1)(y0), given that y0 =...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 14E Ch. 3.10 - Prob. 15E Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 20E Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Tangent lines Find an equation of the line tangent...Ch. 3.10 - Tangent lines Find an equation of the line tangent...Ch. 3.10 - Tangent lines Find an equation of the line tangent...Ch. 3.10 - Tangent lines Find an equation of the line tangent...Ch. 3.10 - Angular size A boat sails directly toward a...Ch. 3.10 - Prob. 36E Ch. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Prob. 39E Ch. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Prob. 43E Ch. 3.10 - Prob. 44E Ch. 3.10 - Slopes of tangent lines Given the function f, find...Ch. 3.10 - Prob. 46E Ch. 3.10 - Prob. 47E Ch. 3.10 - Prob. 48E Ch. 3.10 - Prob. 49E Ch. 3.10 - Prob. 50E Ch. 3.10 - Derivatives of inverse functions from a table Use...Ch. 3.10 - Derivatives of inverse functions from a table Use...Ch. 3.10 - Explain why or why not Determine whether the...Ch. 3.10 - Prob. 54E Ch. 3.10 - Graphing f and f a. Graph f with a graphing...Ch. 3.10 - Prob. 56E Ch. 3.10 - Prob. 57E Ch. 3.10 - Graphing with inverse trigonometric functions a....Ch. 3.10 - Prob. 59E Ch. 3.10 - Prob. 60E Ch. 3.10 - Prob. 61E Ch. 3.10 - Prob. 62E Ch. 3.10 - Prob. 63E Ch. 3.10 - Prob. 64E Ch. 3.10 - Prob. 65E Ch. 3.10 - Prob. 66E Ch. 3.10 - Towing a boat A boat is towed toward a dock by a...Ch. 3.10 - Tracking a dive A biologist standing at the bottom...Ch. 3.10 - Angle to a particle, part I A particle travels...Ch. 3.10 - Prob. 70E Ch. 3.10 - Prob. 71E Ch. 3.10 - Prob. 72E Ch. 3.10 - Prob. 73E Ch. 3.10 - Prob. 74E Ch. 3.10 - Identity proofs Prove the following identities and...Ch. 3.10 - Identity proofs Prove the following identities and...Ch. 3.10 - Identity proofs Prove the following identities and...Ch. 3.10 - Prob. 78E Ch. 3.10 - Prob. 79E Ch. 3.11 - Give an example in which one dimension of a...Ch. 3.11 - Prob. 2E Ch. 3.11 - If two opposite sides of a rectangle increase in...Ch. 3.11 - Prob. 4E Ch. 3.11 - Prob. 5E Ch. 3.11 - Shrinking square The sides of a square decrease in...Ch. 3.11 - Expanding isosceles triangle The legs of an...Ch. 3.11 - Shrinking isosceles triangle The hypotenuse of an...Ch. 3.11 - Expanding circle The area of a circle increases at...Ch. 3.11 - Prob. 10E Ch. 3.11 - Shrinking circle A circle has an initial radius of...Ch. 3.11 - Prob. 12E Ch. 3.11 - Balloons A spherical balloon is inflated and its...Ch. 3.11 - Piston compression A piston is seated at the top...Ch. 3.11 - Melting snowball A spherical snowball melts at a...Ch. 3.11 - Prob. 16E Ch. 3.11 - Prob. 17E Ch. 3.11 - Expanding rectangle A rectangle initially has...Ch. 3.11 - Prob. 19E Ch. 3.11 - Altitude of a jet A jet ascends at a 10 angle from...Ch. 3.11 - Rate of dive of a submarine A surface ship is...Ch. 3.11 - Prob. 22E Ch. 3.11 - Ladder against the wall A 13-foot ladder is...Ch. 3.11 - Ladder against the wall again A 12-foot ladder is...Ch. 3.11 - Moving shadow A 5-foot-tall woman walks at 8 ft/s...Ch. 3.11 - Baseball runners Runners stand at first and second...Ch. 3.11 - Growing sandpile Sand falls from an overhead bin...Ch. 3.11 - Draining a water heater A water heater that has...Ch. 3.11 - Draining a tank An inverted conical water tank...Ch. 3.11 - Drinking a soda At what rate is soda being sucked...Ch. 3.11 - Prob. 31E Ch. 3.11 - Filling a hemispherical tank A hemispherical tank...Ch. 3.11 - Prob. 33E Ch. 3.11 - Observing a launch An observer stands 300 ft from...Ch. 3.11 - Another balloon story A hot-air balloon is 150 ft...Ch. 3.11 - Prob. 36E Ch. 3.11 - Another fishing story An angler hooks a trout and...Ch. 3.11 - Flying a kite Once Kates kite reaches a height of...Ch. 3.11 - Rope on a boat A rope passing through a capstan on...Ch. 3.11 - Parabolic motion An arrow is shot into the air and...Ch. 3.11 - Time-lagged flights An airliner passes over an...Ch. 3.11 - Disappearing triangle An equilateral triangle...Ch. 3.11 - Clock hands The hands of the clock in the tower of...Ch. 3.11 - Filling two pools Two cylindrical swimming pools...Ch. 3.11 - Filming a race A camera is set up at the starting...Ch. 3.11 - Two tanks A conical tank with an upper radius of 4...Ch. 3.11 - Oblique tracking A port and a radar station are 2...Ch. 3.11 - Oblique tracking A ship leaves port traveling...Ch. 3.11 - Watching an elevator An observer is 20 m above the...Ch. 3.11 - A lighthouse problem A lighthouse stands 500 m off...Ch. 3.11 - Prob. 51E Ch. 3.11 - Watching a Ferris wheel An observer stands 20 m...Ch. 3.11 - Viewing angle The bottom of a large theater screen...Ch. 3.11 - Searchlightwide beam A revolving searchlight,...Ch. 3.11 - Draining a trough A trough in the shape of a half...Ch. 3.11 - Divergent paths Two boats leave a port at the same...Ch. 3 - Explain why or why not Determine whether the...Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Growth rate of bacteria Suppose the following...Ch. 3 - Velocity of a skydiver Assume the graph represents...Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Sketching a derivative graph Sketch a graph of f...Ch. 3 - Sketching a derivative graph Sketch a graph of g...Ch. 3 - Matching functions and derivatives Match the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 28RE Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 32RE Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Implicit differentiation Calculate y(x) for the...Ch. 3 - Implicit differentiation Calculate y(x) for the...Ch. 3 - Implicit differentiation Calculate y(x) for the...Ch. 3 - Quadratic functions a. Show that if (a, f(a)) is...Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - A parabola property Let f(x) = x2. a. Show that...Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Derivative formulas Evaluate the following...Ch. 3 - Prob. 50RE Ch. 3 - Derivative formulas Evaluate the following...Ch. 3 - Derivative formulas Evaluate the following...Ch. 3 - Prob. 53RE Ch. 3 - Limits The following limits represent the...Ch. 3 - Limits The following limits represent the...Ch. 3 - Derivative of the inverse at a point Consider the...Ch. 3 - Derivative of the inverse at a point Consider the...Ch. 3 - Derivative of the inverse Find the derivative of...Ch. 3 - Derivative of the inverse Find the derivative of...Ch. 3 - A function and its inverse function The function...Ch. 3 - Prob. 61RE Ch. 3 - Derivatives from a graph If possible, evaluate the...Ch. 3 - Derivatives from a graph If possible, evaluate the...Ch. 3 - Velocity of a probe A small probe is launched...Ch. 3 - Prob. 65RE Ch. 3 - Marginal and average cost Suppose a company...Ch. 3 - Population growth Suppose p(t) = 1.7t3 + 72t2 +...Ch. 3 - Position of a piston The distance between the head...Ch. 3 - Boat rates Two boats leave a dock at the same...Ch. 3 - Rate of inflation of a balloon A spherical balloon...Ch. 3 - Rate of descent of a hot-air balloon A rope is...Ch. 3 - Filling a tank Water flows into a conical tank at...Ch. 3 - Angle of elevation A jet flies horizontally 500 ft...Ch. 3 - Viewing angle A man whose eye level is 6 ft above...

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