Chapter 14: Q. 45 (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.
$c = 3; f (x) = x^{2}$ .

Short Answer

Expert verified

The answer is 6.

Step by step solution

Step. 1 Given Information

$c = 3; f (x) = x^{2} .$

Step. 2 Average rate of change of f.

The average rate of change of f from 3 to x is

$\frac{∆ y}{∆ x} = \frac{f (x) - f (3)}{x - 3} = \frac{(x^{2}) - (3^{2})}{x - 3} = \frac{x^{2} - 9}{x - 3} = \frac{(x - 3) (x + 3)}{(x - 3)} = (x + 3) .$

Step. 3 Finding limit

The limit of the average rate of change is

$\lim_{x \to 3} \frac{∆ y}{∆ x} = \lim_{x \to 3} (x + 3) = 3 + 3 = 6 .$

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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.
$c = 3; f (x) = x^{2}$ .

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Average rate of change of f.

Step. 3 Finding limit

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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=3;f(x)=x2.

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Average rate of change of f.

Step. 3 Finding limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Probability and Statistics

Applied Mathematics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 43–52, find the limit as x approaches c of the average rate of change of each function from c to x.
$c = 3; f (x) = x^{2}$ .