Chapter 4, Problem 20RQ

$\underset{x\to 0}{\lim }\frac{x}{e^x}=1$

To determine

Whether the statement, $\underset{x\to 0}{\lim }\frac{x}{e^x}=1$ is true or false.

Answer to Problem 20RQ

The given statement is false.

Explanation of Solution

The value of $\underset{x\to 0}{\lim }\frac{x}{e^x}$ is obtained as follows.

$\begin{array}{c}\underset{x\to 0}{\lim }\frac{x}{e^x}=\frac{0}{e^0}\\ =\frac{0}{1}\\ =0\end{array}$

Thus, the limit is 0.

Therefore, the given statement is false.