MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review
3rd Edition
ISBN: 9780135243435
Author: Bill Briggs
Publisher: Pearson Education (US)
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Chapter 3.4, Problem 40E
To determine
To find: The derivative of the function.
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Chapter 3 Solutions
MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review
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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- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward
- 2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. B 13 cm 97° Law of Sines Law of Cosines A 43° Then solve the triangle. (Round your answers to two decimal places.) b = x C = A = 40.00arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a 29 b 39 d Ꮎ 126° a Ꮎ b darrow_forward
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