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 3.1, Problem 47E
Explain why or why not Determine whether the following statements are true and give an explanation or counter example
a Far linear functions, the slope of any secant line always equals the slope of any tangent line
b. The slope of the secant line passing through the paints P and Q is less than the slope of the tangent line at P.
c. Consider the graph of the parabola
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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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- Consider the differential equation y'(t)- 2y(t) = 11, y(0) = 3. a. Find a power series for the solution of the differential equation. b. Identify the function represented by the power series. a. Choose the correct answer below. OA. y(t)=3-17t+ 17t 34 (-1)"17.2"-1 3 th + n! OB. y(t)=3+17t+17t 3 34 3 17-27-1 +.. n! OC. y(t) 11-17t+171 = 171² - 3413+ (-1) 17.2"-1 ++ -t t + OD. y(t) = 11+17t+ 17t + b. y(t) = ☐ n! 34 17.2"-1 3 + -t + n!arrow_forwardK Consider the function f(x) = 4 cos x sx. a. Differentiate the Taylor series centered at 0 for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer. 23 35 11 24x 24x OA. -24x 3! 51 17 29 5 24x 24x OC. -24x 21 4! 41 24x 61 b. The differentiated series converges to ☐ (Type an expression using x as the variable.) c. The interval of convergence of the power series for the derivative is (Type your answer in interval notation.) OB G1 EBC 03 TAB 04 CAPS 右邊 CTAL SHIFT 1 This test: 11 point(s) possible This question: 1 point(s) possible 17 29 41 24x OB. -24x5 24x 24x + +... 21 4! 6! OD. - 24x11+ 24x23 31 24x 35 +... 51 ENTER Barrow_forwardFind a power series representation centered at 0 for the following function using known power series. Give the interval of convergence for the resulting series. 4 10x4 f(x) = (1+x5) 2 Which of the following is the power series representation for f(x)? OA. (-1)*2k 5k-1 k=1 00 5k-1 ○ c. Σ (− 1)k+12k•x5k O k=1 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)arrow_forward
- Use the Ratio Test or the Root Test to determine if the following series converges absolutely or diverges. 00 Σ (-17)* k=1 k! Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer in simplified form.) OA. The series converges absolutely by the Ratio Test because r = O B. The series diverges by the Root Test because p= OC. Both tests are inconclusive because r = and p=arrow_forwardUse an appropriate test to determine whether the series converges. 2 Ink Σ k k=2 The series is of the form so by the this series Σf(k) for appropriate f and √ f(x) dx converges, k=2 2 Σa where 0arrow_forward२ Determine whether the following series converges. Σ 2(-1)* 3 k=0k +2 Let ak > 0 represent the magnitude of the terms of the given series. Identify and describe ak Select the correct choice below and fill in any answer box in your choice. OA. ak= OB. ak = O C. ak= and for any index N, there are some values of k > N for which a +12 ak and some values of k > N for which ak+1 ≤ak- is nonincreasing in magnitude for k greater than some index N. is nondecreasing in magnitude for k greater than some index N. Evaluate lim ak- lim ak = k-∞ k-∞ ☐ Does the series converge? O Yes O Noarrow_forward
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