a. Explanation We know that a function is one to one function, if the function never takes on the same value twice that is f ( x 1 ) = f ( x 2 ) , whenever x 1 = x 2 b. To determine How can you tell you from the graph of a function whether it is one-to-one or not?

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

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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Chapter 1.5, Problem 1E

To determine

What is one-to-one function?

To determine

How can you tell you from the graph of a function whether it is one-to-one or not?

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Chapter 1.4, Problem 38E

Chapter 1.5, Problem 2E

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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?

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Does the series converge or diverge

Chapter 1 Solutions

Biocalculus

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What is one-to-one function?

Solution Summary: The author explains that a function is one-to-one function, if it never takes on the same value twice. The functions f(x)=x3 and

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What is one-to-one function?

How can you tell you from the graph of a function whether it is one-to-one or not?

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Chapter 1 Solutions