Chapter 3, Problem 140RE

a.

To determine

To use : the graphing utility to graph the function $y=e^x$ with the graph of each function

Explanation of Solution

Given information : The question is

The function is defined as

  $\begin{array}{l}n!=1·2·\mathrm{3.....}\left(n-1\right)·n\\ y_1=1+\frac{x}{1!}\\ y_2=1+\frac{x}{1!}+\frac{x^2}{2!}\\ y_3=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}\end{array}$

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the data

Step 4: Press $\boxed{\text{GRAPH}}$ button to graph the function.

The graph is obtained as:

  

b.

To determine

To identify : the successive polynomial given in part(a) to extend one more term

Answer to Problem 140RE

The one more term is $y_4=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}$

Explanation of Solution

Given information : the polynomial given in part (a)

  $\begin{array}{l}n!=1·2·\mathrm{3.....}\left(n-1\right)·n\\ y_1=1+\frac{x}{1!}\\ y_2=1+\frac{x}{1!}+\frac{x^2}{2!}\\ y_3=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}\end{array}$

Calculation :

  $\begin{array}{l}{y}_1=1+\frac{x}{1!}\\ y_2=1+\frac{x}{1!}+\frac{x^2}{2!}\\ y_3=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}\\ y_4=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}\end{array}$