Chapter 13.4, Problem 22E

To determine

To find: The graph of the function.

Answer to Problem 22E

The required graph is shown below.

Explanation of Solution

Given:

The function is given by,

  $\underset{x\to \infty }{\lim }{\left(1+\frac{2}{x}\right)}^{3x}$

Calculation:

Let the function $\underset{x\to \infty }{\lim }{\left(1+\frac{2}{x}\right)}^{3x}$ denote as $f\left(x\right)$ . Find the various values of $x$ value of $f\left(x\right)$ for different values of $x$ are listed in table below;

$x$	$f\left(x\right)$
1	27
2	16
3	13.8889
4	13.5
5	13.72
6	14.222
7	14.87777551
8	15.625
9	16.43220988

It is clear from the table that the function $\underset{x\to \infty }{\lim }{\left(1+\frac{2}{x}\right)}^{3x}$ tends to infinity as $x\to \infty$ .

Draw the graph of the function by using this table of values.

  

Therefore, the required graph is shown above.