   Chapter 2.2, Problem 47E ### 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

# (a) Estimate the value of the limit limx→0 (1 + x)1/xto five decimal places. Does this number look familiar?(b) Illustrate part (a) by graphing the function y = (I + x)1/x·

(a)

To determine

To estimate: The value of limx0(1+x)1x by evaluating the value of f(x)=(1+x)1x for various x values that approach 0 from either side and then interpret the resultant limit.

Explanation

As x approaches 1 from either side, evaluate the function f(x)=(1+x)1x for the numbers 0.5,0.1,0.01,0.001,0.0001,0.00001,0.5,0.1,0.01,0.001,0.0001 and 0.00001.

Evaluate the function (correct to 5 decimal places) for the values of x and get the following table of values.

 x (1+x) 1x f(x)=(1+x)1x −0.5 0.5 −2 4 −0.1 0.9 −10 2.86797 −0.01 0.99 −100 2.73200 −0.001 0.999 −1000 2.71964 −0.0001 0.9999 −10000 2

(b)

To determine

To check: The answer obtained in part (a) by graphing the function f(x)=(1+x)1x as x approaches 0 from either side.

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