   Chapter 2.2, Problem 22E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places). lim h → 0 ( 2 + h ) 5 − 32 h , h = ±0.5, ±0.1, ±0.01, ±0.001, ±0.0001

To determine

To guess: The value of limh0(2+h)532h.

Explanation

Given:

The values of h are h=±0.5,±0.1,±0.01,±0.001, and ±0.0001.

Calculation:

Since h approaches 0, the values 0.5,0.1,0.01,0.001, and 0.0001 are to the left of 0 and the values 0.5,0.1,0.01,0.001, and 0.0001 are to the right of 0.

Evaluate the function (correct to 6 decimal places) when h=0.5,0.1,0.01,0.001, and 0.0001 as shown in the below table.

 h (2+h)5 (2+h)5−32 f(h)=(2+h)5−32h −0.5 7.59375 −24.4063 48.812500 −0.1 24.76099 −7.23901 72.390100 −0.01 31.20796 −0.79204 79.203990 −0.001 31.92008 −0.07992 79.920040 −0.0001 31.992 −0.008 79.992000

Here, the value of f(h) approaches 80 as h closer to 0 from the left side.

That is, limh0(2+h)532h=80

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 