Short Answer

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

The limit is $- 1$

See the step by step solution

Step by Step Solution

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TABLE OF CONTENTS

Step 1: Given information

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

Step 2: Calculate the average rate of change using the formula

Calculating, we get

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

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Precalculus Enhanced with Graphing Utilities

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Short Answer

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

Step by Step Solution

Step 1: Given information

Step 2: Calculate the average rate of change using the formula

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Precalculus Enhanced with Graphing Utilities

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Short Answer

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)=1x

Step by Step Solution

Step 1: Given information

Step 2: Calculate the average rate of change using the formula

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