CPM Homework Help : PC3 Problem 13-46

The following limits are slight variations of the limit that is exactly $e$ . With the help of a calculator, express the following limits in terms of $e$ . The $e$ and $e^{x}$ buttons will come in handy.

Hint:

Use a graphing calculator to help you evaluate each of these limits. Each one is a power of $e$ .
Your algebra skills can be used as well. Recall from the lesson:

$\lim_{n\to\infty}\left(1+\frac{a}{n}\right)^n=e^a$

$\lim \limits _ { x \rightarrow \infty } ( 1 + \frac { 1 } { x } ) ^ { 5 x }$
Step (a):
$\lim \limits_{x\to\infty}\left(\left(1+\frac{1}{x}\right)^x\right)^5$

$\lim \limits _ { h \rightarrow \infty } ( 1 - \frac { 1 } { h } ) ^ { h }$
Step (b):
$\lim \limits_{h\to\infty}\left(1+\frac{-1}{h}\right)^h$

$\lim \limits _ { z \rightarrow \infty } ( 1 + \frac { 1 } { 5 z } ) ^ { z }$
Step (c):
$\lim \limits_{z\to\infty}\left(1+\frac{1/5}{z}\right)^z$