Chapter 14: Q. 52 (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 $x$ .
$f (x) = \frac{1}{x^{2}}$

Short Answer

Expert verified

The limit is $- 2$

Step by step solution

Given information

Given function $f (x) = \frac{1}{x^{2}}$

Calculate the average rate of change using the formula

Calculating, we get

$\lim_{x \to c} (\frac{f (x) - f (c)}{x - c}) \lim_{x \to 1} (\frac{\frac{1}{x^{2}} - 1}{x - 1}) = \lim_{x \to 1} (\frac{1 - x^{2}}{x^{2} (x - 1)}) \lim_{x \to 1} (\frac{\frac{1}{x^{2}} - 1}{x - 1}) = \lim_{x \to 1} (- \frac{(x + 1) (x - 1)}{x^{2} (x - 1)}) \lim_{x \to 1} (\frac{\frac{1}{x^{2}} - 1}{x - 1}) = \lim_{x \to 1} (- \frac{x + 1}{x^{2}}) \lim_{x \to 1} (\frac{\frac{1}{x^{2}} - 1}{x - 1}) = - \frac{1 + 1}{1^{2}} \lim_{x \to 1} (\frac{\frac{1}{x^{2}} - 1}{x - 1}) = - 2$

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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 $x$ .
$f (x) = \frac{1}{x^{2}}$

Short Answer

Step by step solution

Given information

Calculate the average rate of change using the formula

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In Problems 43-52, find the limit as xapproaches cof the average rate of change of each function from cto x.f(x)=1x2

Short Answer

Step by step solution

Given information

Calculate the average rate of change using the formula

One App. One Place for Learning.

Most popular questions from this chapter

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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 $x$ .
$f (x) = \frac{1}{x^{2}}$