Calculus, Single Variable: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780134766850
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Textbook Question
Chapter 3.7, Problem 81E
Mass of Juvenile desert tortoises A study conducted at the University of New Mexico found that the mass m(t) (In grams) of a juvenile desert tortoise t days after a switch to a particular diet is described by the function m(t) = m0e0 004t, where m0 is the mass of the tortoise at the time of the diet switch. If m0 = 64, evaluate m′(65) and interpret he nearing of this result.
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Chapter 3 Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Ch. 3.1 - In Example 1, is the slope of the tangent ire at...Ch. 3.1 - Sketch the graph of a function f near a point a....Ch. 3.1 - Set up the calculation in Example 3 using...Ch. 3.1 - Prob. 4QCCh. 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. 4ECh. 3.1 - Prob. 5ECh. 3.1 - The following figure shows the graph of f and a...
Ch. 3.1 - An equation of the line tangent to the graph of f...Ch. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Use definition (1) (p. 133) to find the slope of...Ch. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Prob. 16ECh. 3.1 - Equations of tangent lines by definition (1) a....Ch. 3.1 - Prob. 18ECh. 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. 21ECh. 3.1 - Prob. 22ECh. 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. 26ECh. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Prob. 28ECh. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Prob. 30ECh. 3.1 - Equations of tangent lines by definition (2) a....Ch. 3.1 - Prob. 32ECh. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Prob. 34ECh. 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. 38ECh. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Prob. 40ECh. 3.1 - Derivatives and tangent lines a. For the following...Ch. 3.1 - Prob. 42ECh. 3.1 - Derivative calculations Evaluate the derivative of...Ch. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Explain why or why not Determine whether the...Ch. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Interpreting the derivative Find the derivative of...Ch. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Find the function The following limits represent...Ch. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Find the function The following limits represent...Ch. 3.1 - Find the function The following limits represent...Ch. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.2 - In Example 1, determine the slope of the tangent...Ch. 3.2 - Prob. 2QCCh. 3.2 - Prob. 3QCCh. 3.2 - Prob. 4QCCh. 3.2 - Prob. 5QCCh. 3.2 - Prob. 6QCCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Sketch a graph of a function f, where f(x) 0 and...Ch. 3.2 - Prob. 6ECh. 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 - Describe the graph of f if f(0)=1 and f(x)=3, for...Ch. 3.2 - Prob. 10ECh. 3.2 - Use limits to find f(x) if f(x)=7x.Ch. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Matching functions with derivatives Match graphs...Ch. 3.2 - Prob. 16ECh. 3.2 - Sketching derivatives Reproduce the graph of f and...Ch. 3.2 - Prob. 18ECh. 3.2 - Use the graph of f in the figure to do the...Ch. 3.2 - Prob. 20ECh. 3.2 - Derivatives a.Use limits to find the derivative...Ch. 3.2 - Prob. 22ECh. 3.2 - Derivatives a.Use limits to find the derivative...Ch. 3.2 - Prob. 24ECh. 3.2 - Derivatives a.Use limits to find the derivative...Ch. 3.2 - Prob. 26ECh. 3.2 - Derivatives a.Use limits to find the derivative...Ch. 3.2 - Prob. 28ECh. 3.2 - Derivatives a.Use limits to find the derivative...Ch. 3.2 - Prob. 30ECh. 3.2 - Velocity functions A projectile is fired...Ch. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Tangent lines a.Find the derivative function f for...Ch. 3.2 - Tangent lines a.Find the derivative function f for...Ch. 3.2 - Calculating derivatives a. For the following...Ch. 3.2 - Prob. 38ECh. 3.2 - Calculating derivatives a. For the following...Ch. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Analyzing slopes Use the points A, B, C, D, and E...Ch. 3.2 - Prob. 46ECh. 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 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Where is the function continuous? Differentiable?...Ch. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 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 - Normal lines A line perpendicular to another line...Ch. 3.2 - Aiming a tangent line Given the function f and the...Ch. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Continuity is necessary for differentiability a....Ch. 3.2 - Prob. 78ECh. 3.3 - Find the values of ddx(11) and ddx()Ch. 3.3 - Prob. 2QCCh. 3.3 - Prob. 3QCCh. 3.3 - Prob. 4QCCh. 3.3 - Prob. 5QCCh. 3.3 - Prob. 6QCCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Given that f(3) = 6 and g(3) = 2, find (f + g)(3).Ch. 3.3 - Prob. 8ECh. 3.3 - Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and...Ch. 3.3 - Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and...Ch. 3.3 - Let F(x)=f(x)+g(x),G(x)=f(x)g(x), and...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 - If f(t)=t10, find f(t),f(t), and f(t).Ch. 3.3 - Prob. 16ECh. 3.3 - The line tangent to the graph of f at x = 5 is...Ch. 3.3 - Prob. 18ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 24ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 26ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 28ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 30ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 32ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 38ECh. 3.3 - Derivatives Find the derivative of the following...Ch. 3.3 - Prob. 40ECh. 3.3 - Height estimate The distance an object falls (when...Ch. 3.3 - Prob. 42ECh. 3.3 - City urbanization City planners model the size of...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Derivatives of products and quotients Find the...Ch. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Prob. 48ECh. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Prob. 50ECh. 3.3 - Derivatives of products and quotients Find the...Ch. 3.3 - Prob. 52ECh. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Prob. 54ECh. 3.3 - Derivatives of products Find the derivative of the...Ch. 3.3 - Prob. 56ECh. 3.3 - Derivatives of products and quotients Find the...Ch. 3.3 - Prob. 58ECh. 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 - Prob. 62ECh. 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 - Prob. 66ECh. 3.3 - Finding slope locations Let f(x)=4xx. a. Find all...Ch. 3.3 - Prob. 68ECh. 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 - Prob. 71ECh. 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 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 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 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.3 - Derivatives from a graph Let F = f + g and G = 3f ...Ch. 3.3 - Prob. 82ECh. 3.3 - Prob. 83ECh. 3.3 - Prob. 84ECh. 3.3 - Prob. 85ECh. 3.3 - Prob. 86ECh. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Prob. 90ECh. 3.3 - Prob. 91ECh. 3.3 - Prob. 92ECh. 3.3 - Prob. 93ECh. 3.3 - Prob. 94ECh. 3.3 - Prob. 95ECh. 3.3 - Prob. 96ECh. 3.3 - Prob. 97ECh. 3.3 - Prob. 98ECh. 3.4 - Find the derivative of f(x) = x5. Then find the...Ch. 3.4 - Prob. 2QCCh. 3.4 - Prob. 3QCCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Derivatives by two different methods a. Use the...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 22ECh. 3.4 - Derivatives Find and simplify the derivative of...Ch. 3.4 - Prob. 24ECh. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 26ECh. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 28ECh. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 30ECh. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Prob. 32ECh. 3.4 - Derivatives of products Find the derivative of the...Ch. 3.4 - Prob. 34ECh. 3.4 - Derivatives Find and simplify the derivative of...Ch. 3.4 - Prob. 36ECh. 3.4 - Derivatives of quotients Find the derivative of...Ch. 3.4 - Prob. 38ECh. 3.4 - Extended Power Rule Find the derivative of the...Ch. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Choose your method Use any method to evaluate the...Ch. 3.4 - Prob. 57ECh. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - Derivatives Find and simplify the derivative of...Ch. 3.4 - Equations of tangent lines a. Find an equation of...Ch. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Explain why or why not Determine whether the...Ch. 3.4 - Prob. 70ECh. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - First and second derivatives Find f(x) and f(x)....Ch. 3.4 - Tangent lines Suppose f(2) = 2 and f(2) = 3. Let...Ch. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Derivatives from a table Use the following table...Ch. 3.4 - Prob. 82ECh. 3.4 - Prob. 83ECh. 3.4 - Prob. 84ECh. 3.4 - Prob. 85ECh. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - Prob. 89ECh. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3.4 - Prob. 94ECh. 3.4 - Prob. 95ECh. 3.4 - Prob. 96ECh. 3.4 - Prob. 97ECh. 3.4 - Prob. 98ECh. 3.4 - Prob. 99ECh. 3.5 - Evaluate limx0tan2xxCh. 3.5 - Prob. 2QCCh. 3.5 - Prob. 3QCCh. 3.5 - Prob. 4QCCh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Where does the graph of sin x have a horizontal...Ch. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 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 - Prob. 16ECh. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Prob. 18ECh. 3.5 - Trigonometric limits Use Theorem 3.11 to evaluate...Ch. 3.5 - Prob. 20ECh. 3.5 - Trigonometric limits Evaluate the following limits...Ch. 3.5 - Prob. 22ECh. 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. 26ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 28ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 30ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Calculating derivatives Find the derivative of the...Ch. 3.5 - Prob. 36ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 38ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 40ECh. 3.5 - Calculating derivatives Find dy/dx for the...Ch. 3.5 - Prob. 42ECh. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Derivatives involving other trigonometric...Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Explain why or why not Determine whether the...Ch. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.5 - Prob. 73ECh. 3.5 - Prob. 74ECh. 3.5 - Prob. 75ECh. 3.5 - Prob. 76ECh. 3.5 - Prob. 77ECh. 3.5 - Prob. 78ECh. 3.5 - Prob. 79ECh. 3.5 - Prob. 80ECh. 3.5 - Proof of limx0cosx1x=0 Use the trigonometric...Ch. 3.5 - Prob. 82ECh. 3.5 - Prob. 83ECh. 3.5 - Prob. 84ECh. 3.5 - Prob. 85ECh. 3.5 - Prob. 86ECh. 3.5 - Prob. 87ECh. 3.5 - Prob. 88ECh. 3.5 - Prob. 89ECh. 3.5 - Prob. 90ECh. 3.6 - Does the speedometer in your car measure average...Ch. 3.6 - Prob. 2QCCh. 3.6 - Describe the velocity of an object that has a...Ch. 3.6 - Prob. 4QCCh. 3.6 - Prob. 5QCCh. 3.6 - Prob. 6QCCh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Suppose the function s(t) represents the position...Ch. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Define the acceleration of an object moving in a...Ch. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Prob. 16ECh. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Position, velocity, and acceleration Suppose the...Ch. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - A dropped stone on Earth The height (in feet) of a...Ch. 3.6 - A dropped stone on Mars A stone is dropped off the...Ch. 3.6 - Throwing a stone Suppose a stone is thrown...Ch. 3.6 - Suppose a stone is thrown vertically upward from...Ch. 3.6 - A stone thrown vertically on Mars Suppose a stone...Ch. 3.6 - Maximum height Suppose a baseball is thrown...Ch. 3.6 - Initial velocity Suppose a baseball is thrown...Ch. 3.6 - Prob. 28ECh. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Prob. 30ECh. 3.6 - Average and marginal cost Consider the following...Ch. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Explain why or why not Determine whether the...Ch. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Matching heights A stone is thrown from the edge...Ch. 3.6 - Prob. 40ECh. 3.6 - Velocity from position The graph of s = f(t)...Ch. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Diminishing returns A cost function of the form...Ch. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Spring oscillations A spring hangs from the...Ch. 3.6 - Prob. 56ECh. 3.6 - A race Jean and Juan run a one-lap race on a...Ch. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - Prob. 60ECh. 3.6 - Prob. 61ECh. 3.7 - Explain why it is not practical to calculate...Ch. 3.7 - Prob. 2QCCh. 3.7 - Prob. 3QCCh. 3.7 - Two equivalent forms of the Chain Rule for...Ch. 3.7 - Prob. 2ECh. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21ECh. 3.7 - Prob. 22ECh. 3.7 - Prob. 23ECh. 3.7 - Prob. 24ECh. 3.7 - Chain Rule using a table Let h(x)= f(g(x)) and...Ch. 3.7 - Prob. 26ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 28ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 30ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 32ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 34ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 36ECh. 3.7 - Version 2 of the Chain Rule Use Version 2 of the...Ch. 3.7 - Prob. 38ECh. 3.7 - Calculate the derivative of the following...Ch. 3.7 - Prob. 40ECh. 3.7 - Prob. 41ECh. 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 - Chain Rule for powers Use the Chain Rule to find...Ch. 3.7 - Prob. 46ECh. 3.7 - Calculate the derivative of the following...Ch. 3.7 - Prob. 48ECh. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Prob. 50ECh. 3.7 - Prob. 51ECh. 3.7 - Prob. 52ECh. 3.7 - Repeated use of the Chain Rule Calculate the...Ch. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.7 - Prob. 57ECh. 3.7 - Prob. 58ECh. 3.7 - Prob. 59ECh. 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. 62ECh. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 64ECh. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 66ECh. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 68ECh. 3.7 - Combining rules Use the Chain Rule combined with...Ch. 3.7 - Prob. 70ECh. 3.7 - Calculate the derivative of the following...Ch. 3.7 - Prob. 72ECh. 3.7 - Calculate the derivative of the following...Ch. 3.7 - Prob. 74ECh. 3.7 - Square root derivatives Find the derivative of the...Ch. 3.7 - Prob. 76ECh. 3.7 - Explain why or why not Determine whether the...Ch. 3.7 - Prob. 78ECh. 3.7 - Applying the Chain Rule Use the data in Tables 3.4...Ch. 3.7 - Mass of Juvenile desert tortoises A study...Ch. 3.7 - Prob. 82ECh. 3.7 - Prob. 83ECh. 3.7 - Pressure and altitude Earths atmospheric pressure...Ch. 3.7 - Finding slope locations Let f(x) = xe2x. a. Find...Ch. 3.7 - Prob. 86ECh. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Prob. 88ECh. 3.7 - Second derivatives Find d2ydx2 for the following...Ch. 3.7 - Prob. 90ECh. 3.7 - Prob. 91ECh. 3.7 - Prob. 92ECh. 3.7 - Tangent lines Assume f and g are differentiable on...Ch. 3.7 - Tangent lines Assume f is a differentiable...Ch. 3.7 - Prob. 95ECh. 3.7 - Prob. 96ECh. 3.7 - Prob. 97ECh. 3.7 - Prob. 98ECh. 3.7 - Prob. 99ECh. 3.7 - Prob. 100ECh. 3.7 - Prob. 101ECh. 3.7 - Prob. 102ECh. 3.7 - Prob. 103ECh. 3.7 - A mixing tank A 500-liter (L) tank is filled with...Ch. 3.7 - Power and energy The total energy in megawatt-hr...Ch. 3.7 - Prob. 106ECh. 3.7 - Prob. 107ECh. 3.7 - Prob. 108ECh. 3.7 - Prob. 109ECh. 3.7 - Prob. 110ECh. 3.7 - Prob. 111ECh. 3.7 - Prob. 112ECh. 3.7 - Prob. 113ECh. 3.7 - Prob. 114ECh. 3.7 - Prob. 115ECh. 3.8 - The equation x y2 = 0 implicitly defines what two...Ch. 3.8 - Use implicit differentiation to find dydx for x ...Ch. 3.8 - Prob. 3QCCh. 3.8 - For some equations, such as x2 + y2 = l or x y2 =...Ch. 3.8 - Prob. 2ECh. 3.8 - Why are both the x-coordinate and the y-coordinate...Ch. 3.8 - Prob. 4ECh. 3.8 - Calculate dydx using implicit differentiation....Ch. 3.8 - Prob. 6ECh. 3.8 - Calculate dydx using implicit differentiation. 7....Ch. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Consider the curve x=y3. Use implicit...Ch. 3.8 - Prob. 12ECh. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Prob. 15ECh. 3.8 - Implicit differentiation Carry out the following...Ch. 3.8 - Prob. 17ECh. 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 Carry out the following...Ch. 3.8 - Prob. 27ECh. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Prob. 29ECh. 3.8 - Prob. 30ECh. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Implicit differentiation Use implicit...Ch. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - Prob. 35ECh. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - Prob. 38ECh. 3.8 - Prob. 39ECh. 3.8 - Prob. 40ECh. 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 - Tangent lines Carry out the following steps....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. 48ECh. 3.8 - Prob. 49ECh. 3.8 - Tangent lines Carry out the following steps. a....Ch. 3.8 - Second derivatives Find d2ydx2. 31. x + y2 = 1Ch. 3.8 - Second derivatives Find d2ydx2. 32. 2x2 + y2 = 4Ch. 3.8 - Second derivatives Find d2ydx2. 33. x + y = sin yCh. 3.8 - Second derivatives Find d2ydx2. 34. x4 + y4 = 64Ch. 3.8 - Second derivatives Find d2ydx2. 35. e2y + x = yCh. 3.8 - Second derivatives Find d2ydx2 36. sin x + x2y =...Ch. 3.8 - Explain why or why not Determine whether the...Ch. 3.8 - Carry out the following steps. a.Use implicit...Ch. 3.8 - Carry out the following steps. a.Use implicit...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. 68ECh. 3.8 - Prob. 69ECh. 3.8 - Identifying functions from an equation The...Ch. 3.8 - Prob. 71ECh. 3.8 - Prob. 72ECh. 3.8 - Prob. 73ECh. 3.8 - Prob. 74ECh. 3.8 - Prob. 75ECh. 3.8 - Prob. 76ECh. 3.8 - Prob. 77ECh. 3.8 - Prob. 78ECh. 3.8 - Prob. 79ECh. 3.8 - Prob. 80ECh. 3.8 - Prob. 81ECh. 3.8 - Prob. 82ECh. 3.8 - Prob. 83ECh. 3.8 - Prob. 84ECh. 3.8 - Prob. 85ECh. 3.8 - Prob. 86ECh. 3.8 - Prob. 87ECh. 3.8 - Prob. 88ECh. 3.8 - Prob. 89ECh. 3.8 - Prob. 90ECh. 3.8 - Prob. 91ECh. 3.8 - Prob. 92ECh. 3.8 - Prob. 93ECh. 3.9 - Simplify e2 ln x. Express 5x using toe base e.Ch. 3.9 - Find ddx(lnxp), where x 0 and p is a real number...Ch. 3.9 - Prob. 3QCCh. 3.9 - Prob. 4QCCh. 3.9 - Prob. 5QCCh. 3.9 - Use x = ey to explain why ddx(lnx)=1x, for x 0.Ch. 3.9 - Prob. 2ECh. 3.9 - Prob. 3ECh. 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 bCh. 3.9 - Simplify the expression exln(x2+1).Ch. 3.9 - Prob. 8ECh. 3.9 - Find ddx(lnx2+1).Ch. 3.9 - Evaluate ddx(xe+ex)Ch. 3.9 - Express the function f(x)=f(x)h(x) in terms of the...Ch. 3.9 - Prob. 12ECh. 3.9 - Prob. 13ECh. 3.9 - Prob. 14ECh. 3.9 - Prob. 15ECh. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Prob. 17ECh. 3.9 - Prob. 18ECh. 3.9 - Prob. 19ECh. 3.9 - Prob. 20ECh. 3.9 - Prob. 21ECh. 3.9 - Prob. 22ECh. 3.9 - Derivatives involving ln x Find the following...Ch. 3.9 - Prob. 24ECh. 3.9 - Prob. 25ECh. 3.9 - Prob. 26ECh. 3.9 - Derivatives Find the derivative of the following...Ch. 3.9 - Prob. 28ECh. 3.9 - Prob. 29ECh. 3.9 - Derivatives Find the derivative of the following...Ch. 3.9 - Prob. 31ECh. 3.9 - Prob. 32ECh. 3.9 - Prob. 33ECh. 3.9 - Prob. 34ECh. 3.9 - Prob. 35ECh. 3.9 - Prob. 36ECh. 3.9 - Prob. 37ECh. 3.9 - Prob. 38ECh. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Prob. 40ECh. 3.9 - Prob. 41ECh. 3.9 - Prob. 42ECh. 3.9 - Prob. 43ECh. 3.9 - Prob. 44ECh. 3.9 - Derivatives of bx Find the derivatives of the...Ch. 3.9 - Prob. 46ECh. 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 - Prob. 50ECh. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Prob. 52ECh. 3.9 - Prob. 53ECh. 3.9 - Derivatives of Tower Functions (or gh) Find the...Ch. 3.9 - Prob. 55ECh. 3.9 - Prob. 56ECh. 3.9 - Prob. 57ECh. 3.9 - Prob. 58ECh. 3.9 - Find an equation of the line tangent to y = xsin x...Ch. 3.9 - Prob. 60ECh. 3.9 - The graph of y = (x2)x has two horizontal tangent...Ch. 3.9 - Prob. 62ECh. 3.9 - Prob. 63ECh. 3.9 - Derivatives of logarithmic functions Calculate the...Ch. 3.9 - Prob. 65ECh. 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 Use the...Ch. 3.9 - Prob. 70ECh. 3.9 - Prob. 71ECh. 3.9 - Derivatives of logarithmic functions Use the...Ch. 3.9 - Prob. 73ECh. 3.9 - Prob. 74ECh. 3.9 - General logarithmic and exponential derivatives...Ch. 3.9 - Prob. 76ECh. 3.9 - Prob. 77ECh. 3.9 - Prob. 78ECh. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Prob. 80ECh. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Prob. 83ECh. 3.9 - Prob. 84ECh. 3.9 - Logarithmic differentiation Use logarithmic...Ch. 3.9 - Prob. 86ECh. 3.9 - Prob. 87ECh. 3.9 - Prob. 88ECh. 3.9 - Prob. 89ECh. 3.9 - Higher-order derivatives Find the following...Ch. 3.9 - Prob. 91ECh. 3.9 - Prob. 92ECh. 3.9 - Prob. 93ECh. 3.9 - Prob. 94ECh. 3.9 - Prob. 95ECh. 3.9 - Prob. 96ECh. 3.9 - Prob. 97ECh. 3.9 - Prob. 98ECh. 3.9 - Prob. 99ECh. 3.9 - Prob. 100ECh. 3.9 - Prob. 101ECh. 3.9 - Prob. 102ECh. 3.9 - Prob. 103ECh. 3.9 - Prob. 104ECh. 3.9 - Prob. 105ECh. 3.9 - Prob. 106ECh. 3.9 - Prob. 107ECh. 3.9 - Prob. 108ECh. 3.9 - Prob. 109ECh. 3.9 - Prob. 110ECh. 3.10 - Is f(x) = sin1x an even or odd function? Is f(x)...Ch. 3.10 - Prob. 2QCCh. 3.10 - Prob. 3QCCh. 3.10 - Prob. 4QCCh. 3.10 - Prob. 5QCCh. 3.10 - Prob. 1ECh. 3.10 - Prob. 2ECh. 3.10 - Prob. 3ECh. 3.10 - Prob. 4ECh. 3.10 - Suppose f is a one-to-one function with f(2) = 8...Ch. 3.10 - Prob. 6ECh. 3.10 - Prob. 7ECh. 3.10 - Prob. 8ECh. 3.10 - If f is a one-to-one function with f(3) = 8 and...Ch. 3.10 - The line tangent to the graph of the one-to-one...Ch. 3.10 - Find the slope of the curve y = sin1x at...Ch. 3.10 - Prob. 12ECh. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Prob. 14ECh. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Prob. 16ECh. 3.10 - Derivatives of inverse sine Evaluate the...Ch. 3.10 - Prob. 18ECh. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 20ECh. 3.10 - Prob. 21ECh. 3.10 - Prob. 22ECh. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 24ECh. 3.10 - Evaluate the derivative of the following...Ch. 3.10 - Prob. 26ECh. 3.10 - Evaluate the derivative of the following...Ch. 3.10 - Prob. 28ECh. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 30ECh. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 32ECh. 3.10 - Prob. 33ECh. 3.10 - Prob. 34ECh. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Derivatives Evaluate the derivatives of the...Ch. 3.10 - Prob. 37ECh. 3.10 - Prob. 38ECh. 3.10 - Prob. 39ECh. 3.10 - Prob. 40ECh. 3.10 - Prob. 41ECh. 3.10 - Prob. 42ECh. 3.10 - Prob. 43ECh. 3.10 - Prob. 44ECh. 3.10 - Prob. 45ECh. 3.10 - Prob. 46ECh. 3.10 - Derivatives of inverse functions at a point Find...Ch. 3.10 - Prob. 48ECh. 3.10 - Prob. 49ECh. 3.10 - Prob. 50ECh. 3.10 - Prob. 51ECh. 3.10 - Prob. 52ECh. 3.10 - Prob. 53ECh. 3.10 - Prob. 54ECh. 3.10 - Prob. 55ECh. 3.10 - Prob. 56ECh. 3.10 - Prob. 57ECh. 3.10 - Prob. 58ECh. 3.10 - Prob. 59ECh. 3.10 - Prob. 60ECh. 3.10 - Prob. 61ECh. 3.10 - Prob. 62ECh. 3.10 - Prob. 63ECh. 3.10 - Prob. 64ECh. 3.10 - Prob. 65ECh. 3.10 - Prob. 66ECh. 3.10 - Derivatives of inverse functions Consider the...Ch. 3.10 - Prob. 68ECh. 3.10 - Derivatives of inverse functions Consider the...Ch. 3.10 - Prob. 70ECh. 3.10 - Prob. 71ECh. 3.10 - Prob. 72ECh. 3.10 - Prob. 73ECh. 3.10 - Prob. 74ECh. 3.10 - Prob. 75ECh. 3.10 - Prob. 76ECh. 3.10 - Derivatives of inverse functions Consider the...Ch. 3.10 - Prob. 78ECh. 3.10 - Prob. 79ECh. 3.10 - Tracking a dive A biologist standing at the bottom...Ch. 3.10 - Prob. 81ECh. 3.10 - Prob. 82ECh. 3.10 - Prob. 83ECh. 3.10 - Prob. 84ECh. 3.10 - Derivative of cot1 x and csc1 x Use a...Ch. 3.10 - Prob. 86ECh. 3.10 - Prob. 87ECh. 3.10 - Prob. 88ECh. 3.10 - Prob. 89ECh. 3.10 - Prob. 90ECh. 3.11 - Prob. 1QCCh. 3.11 - Prob. 2QCCh. 3.11 - Prob. 3QCCh. 3.11 - Prob. 4QCCh. 3.11 - Give an example in which one dimension of a...Ch. 3.11 - Charles law states that for a fixed mass of gas...Ch. 3.11 - If two opposite sides of a rectangle increase in...Ch. 3.11 - Prob. 4ECh. 3.11 - A rectangular swimming pool 10 ft wide by 20 ft...Ch. 3.11 - Prob. 6ECh. 3.11 - The volume V of a sphere of radius r changes over...Ch. 3.11 - At all times, the length of the long leg of a...Ch. 3.11 - Prob. 9ECh. 3.11 - Assume w=x2y4, where x and y are functions of t....Ch. 3.11 - Prob. 11ECh. 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. 16ECh. 3.11 - Shrinking circle A circle has an initial radius of...Ch. 3.11 - Prob. 18ECh. 3.11 - Prob. 19ECh. 3.11 - Expanding rectangle A rectangle initially has...Ch. 3.11 - Prob. 21ECh. 3.11 - Divergent paths Two beats leave a pert at the same...Ch. 3.11 - Time-lagged flights An airliner passes over an...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 - Bug on a parabola A bug is moving along the right...Ch. 3.11 - Prob. 27ECh. 3.11 - Baseball runners Runners stand at first and second...Ch. 3.11 - Another fishing story An angler hooks a trout and...Ch. 3.11 - Prob. 30ECh. 3.11 - Draining a water heater A water heater that has...Ch. 3.11 - Drinking a soda At what rate is soda being sucked...Ch. 3.11 - Prob. 33ECh. 3.11 - Filling two pools Two cylindrical swimming pools...Ch. 3.11 - Growing sandpile Sand falls from an overhead bin...Ch. 3.11 - Draining a tank An inverted conical water tank...Ch. 3.11 - Prob. 37ECh. 3.11 - Two tanks A conical tank with an upper radius of 4...Ch. 3.11 - Prob. 39ECh. 3.11 - Prob. 40ECh. 3.11 - Ladder against the wall A 13-foot ladder is...Ch. 3.11 - Prob. 42ECh. 3.11 - Moving shadow A 5-foot-tall woman walks at 8 ft/s...Ch. 3.11 - Prob. 44ECh. 3.11 - Watching an elevator An observer is 20 m above the...Ch. 3.11 - Prob. 46ECh. 3.11 - Prob. 47ECh. 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 - A lighthouse problem A lighthouse stands 500 m off...Ch. 3.11 - Filming a race A camera is set up at the starting...Ch. 3.11 - Prob. 52ECh. 3.11 - Prob. 53ECh. 3.11 - Prob. 54ECh. 3.11 - Prob. 55ECh. 3.11 - Prob. 56ECh. 3.11 - Filling a pool A swimming pool is 50 m long and 20...Ch. 3.11 - Prob. 58ECh. 3.11 - Prob. 59ECh. 3.11 - Oblique tracking A ship leaves port traveling...Ch. 3.11 - Prob. 61ECh. 3.11 - Prob. 62ECh. 3.11 - Prob. 63ECh. 3.11 - Prob. 64ECh. 3 - Explain why or why not Determine whether the...Ch. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Evaluate and simplify y'. 10.y=4x4lnxx4Ch. 3 - Evaluate and simplify y'. 11.y=2xCh. 3 - Prob. 12RECh. 3 - Evaluate and simplify y'. 13.y=e2Ch. 3 - Prob. 14RECh. 3 - Evaluate and simplify y'. 15.y=(1+x4)3/2Ch. 3 - Prob. 16RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 18RECh. 3 - Evaluate and simplify y'. 19.y=ex(x2+2x+2)Ch. 3 - Prob. 20RECh. 3 - Evaluate and simplify y'. 21.y=sec2wsec2w+1Ch. 3 - Prob. 22RECh. 3 - Evaluate and simplify y'. 23.y=ln|sec3x|Ch. 3 - Prob. 24RECh. 3 - Evaluate and simplify y'. 25.y=(5t2+10)100Ch. 3 - Prob. 26RECh. 3 - Evaluate and simplify y'. 27.y=ln(sinx3)Ch. 3 - Prob. 28RECh. 3 - Evaluate and simplify y'. 29.y=tan1t21Ch. 3 - Prob. 30RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 32RECh. 3 - Evaluate and simplify y'. 33.y=lnww5Ch. 3 - Prob. 34RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 36RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 38RECh. 3 - Evaluate and simplify y'. 39.y=sincos2x+1Ch. 3 - Prob. 40RECh. 3 - Evaluate and simplify y'. 41.y=lnet+1Ch. 3 - Prob. 42RECh. 3 - Evaluate and simplify y'. 43.y=x2+2xtan1(cotx)Ch. 3 - Prob. 44RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 46RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 48RECh. 3 - Evaluate and simplify y'. 49.y=(x2+1)lnxCh. 3 - Prob. 50RECh. 3 - Evaluating derivatives Evaluate and simplify the...Ch. 3 - Prob. 52RECh. 3 - Evaluate and simplify y'. 53.y=6xcot13x+ln(9x2+1)Ch. 3 - Prob. 54RECh. 3 - Evaluate and simplify y'. 55.x=cos(xy)Ch. 3 - Prob. 56RECh. 3 - Implicit differentiation Calculate y(x) for the...Ch. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Tangent lines Find an equation of the line tangent...Ch. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Antibiotic decay The half-life of an antibiotic in...Ch. 3 - Population of the United States The population of...Ch. 3 - Prob. 100RECh. 3 - Velocity of a skydiver Assume the graph represents...Ch. 3 - Prob. 102RECh. 3 - Prob. 103RECh. 3 - Prob. 104RECh. 3 - Prob. 105RECh. 3 - Prob. 106RECh. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Boat rates Two boats leave a dock at the same...Ch. 3 - Prob. 112RECh. 3 - Prob. 113RECh. 3 - Prob. 114RECh. 3 - Prob. 115RECh. 3 - Prob. 116RECh. 3 - Prob. 117RECh. 3 - Prob. 118RECh. 3 - Prob. 119RECh. 3 - Prob. 120RE
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- The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forward
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- Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.arrow_forwardRepeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.arrow_forward10) The Hurricane Hunters took the following measurements from a hurricane over They found that the air pressure and wind speed are related in the following way: y=-1.11x+1140 where x is the air pressure in millibars (kPa) and y is the maximum sustained wind speed in knots (nautical miles per hour). several days as it developed: Air Pressure (kPa) Wind Speed (knots) 924 129 933 110 946 67.3 140 958 86 120 991 41.3 100 1,002 35.7 車 920 910 Air Pressure (kPa) a) What does the y-intercept of this function represent? b) Using the model, what would be the wind speed of a hurricane with an air pressure of 969 kPa? Round your answer to the nearest knot. Wind Speed (knots)arrow_forward
- A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.67 0.70 0.93 0.95 1.09 1.01 1.29 1.24 1.41 1.56 1.73 1.80 Units of BCI (Y) 14.4 20.9 16.2 25.0 18.9 19.8 20.7 22.1 23.9 24.9 27.6 29.7 Find the correlation coefficient between pH and BCI (round to the nearest hundredth; place your answer in the box below)arrow_forwardThe standard error of the constant isarrow_forwardA group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.65 0.75 0.89 0.94 1.12 1.16 1.29 1.35 1.48 1.56 1.73 1.80 Units of BCI (Y) 16.0 18.9 15.6 21.1 23.6 24.9 26.1 29.2 19.3 30.7 33.7 29.4 Find the coefficient of determination between pH and BCI (round to the nearest hundredth; place your answer in the box below)arrow_forward
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