BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.2, Problem 27E

(a)

To determine

To find:

The value of given limit at that every point .

Expert Solution

Answer to Problem 27E

  limx0f(x)=2.71828

Explanation of Solution

Given:

The function f is

  limx0(1+x)1x

Concept used:

Let f(x) be a function defined on an interval that contains x=a , except possibly at x=a

Then

  limxaf(x)=L

Calculation:

The existence of the limit

  limx0(1+x)1x

Apply by the limit and using the value of the given limit

  limx0f(x)=limx0(1+x)1xlimx0f(x)=elimx0f(x)=2.71828

(b)

To determine

To sketch:

The graph of the given function .

Expert Solution

Explanation of Solution

Given:

The function f is

  limx0(1+x)1x

Concept used:

Let f(x) be a function defined on an interval that contains x=a , except possibly at x=a

Then

  limxaf(x)=L

Calculation:

The existence of the limit

  f(x)=(1+x)1x

Test one point in each of the region formed by the graph

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function .

To draw the table

  f(x)=(1+x)1x

    xaxis10.134
    yaxis22.51.51.44

To draw a graph

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 27E

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