# How the number e is defined.

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 1.5, Problem 6E

(a)

To determine

## How the number e is defined.

Expert Solution

### Explanation of Solution

The number e can be defined in the following ways.

limx(1+1x)x=e and n=0xnn!=e .

(b)

To determine

Expert Solution

### Explanation of Solution

An approximate value of e, rounded off to five decimal places is e=2.71828 .

(c)

To determine

Expert Solution

### Explanation of Solution

The function y=ex is said to be the natural exponential function with base e and an exponent x.

The graph of y=ex is lies between the graph of y=2x and y=3x as the value of e is 2.71828.

The graph of exponential function always passes through the point (0,1) as any number raised to the power 0 is 1.

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