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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 51 (page 883)

In Problems 43-52, find the limit as $x$ approaches $c$ of the average rate of change of each function from $c$ to $x$ .
$c = 1; f (x) = \frac{1}{x}$

Short Answer

Expert verified

The limit is $- 1$

Step by step solution

01

Given information

Given the function $f (x) = \frac{1}{x}$

02

Calculate the average rate of change using the formula

Calculating, we get

$\lim_{x 鈫� c} (\frac{f (x) - f (c)}{x - c}) \lim_{x 鈫� 1} (\frac{\frac{1}{x} - 1}{x - 1}) = \lim_{x 鈫� 1} (- \frac{1 - x}{x (- x + 1)}) \lim_{x 鈫� 1} (\frac{\frac{1}{x} - 1}{x - 1}) = = \lim_{x 鈫� 1} (- \frac{1}{x}) \lim_{x 鈫� 1} (\frac{\frac{1}{x} - 1}{x - 1}) = - \frac{1}{1} \lim_{x 鈫� 1} (\frac{\frac{1}{x} - 1}{x - 1}) = - 1$

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Most popular questions from this chapter

Use a graphing utility to find the indicated limit rounded to two decimal places.

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