Chapter 12.7, Problem 2CFU

To determine

To find: the value of $x$ by using the graph.

Answer to Problem 2CFU

  $-1.5\le x\le 2$

Explanation of Solution

Given information:

The series $1+x+\frac{x^2}{2}+\frac{x^3}{6}$ gives a good approximation of function $e^x$ .

The graph is shown below.

  

Calculation:

The interval where the red graph is identical to the blue graph will give the value of $x$ for which the series is a good approximation of $e^x$ . Thus, the interval is $-1.5\le x\le 2$ .