Bundle: Applied Calculus, Loose-leaf Version, 7th + Webassign Printed Access Card For Waner/costenoble's Applied Calculus, 7th Edition, Single-term

7th Edition

ISBN: 9781337604703

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Textbook Question

Chapter 1.1, Problem 9E

In Exercises 9-12, say whether or not f ( x ) is defined for the given values of x. If it is defined, give its value. [Hint: See Quick Example 3.]

f ( x ) = x − 1 x 2 , with its natural domain

a. x = 4

b. x = 0

c. x = − 1

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Chapter 1.1, Problem 8E

Chapter 1.1, Problem 10E

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Does the series converge or diverge

Chapter 1 Solutions

Bundle: Applied Calculus, Loose-leaf Version, 7th + Webassign Printed Access Card For Waner/costenoble's Applied Calculus, 7th Edition, Single-term

Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - In Exercises 1-4, evaluate each expression based...Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - In Exercises 5-8, use the graph of the function f...Ch. 1.1 - Prob. 8E Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...Ch. 1.1 - In Exercises 9-12, say whether or not f(x) is...

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In Exercises 9-12, say whether or not f ( x ) is defined for the given values of x. If it is defined, give its value. [ Hint: See Quick Example 3.] f ( x ) = x − 1 x 2 , with its natural domain a. x = 4 b. x = 0 c. x = − 1

Solution Summary: The author explains that the function f(x) is defined at x=4 in its natural domain. If it is not defined give its value.

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Chapter 1 Solutions