Chapter 2.2, Problem 65E

### Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

Chapter
Section

### Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
Textbook Problem

# Estimating a Limit Consider the function f ( x ) = ( 1 + x ) 1 / x ⋅ Estimate lim x → 0 ( 1 + x ) 1 / x by evaluating f at x-values near 0. Sketch the graph of f.

To determine

To Graph: Sketch the graph of the limit of the function f(x)=(1+x)1/x

Explanation

 X -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) 2.86797 2.73199 2.71964 2.71694 2.70481 2.59374

From the above table and graph, we could say that the value of the limit is 2.72. This is because f(x) approaches a unique value as X approaches 0 from either right or left.

Given: Function: f(x)=(1+x)1/x

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