Chapter 11, Problem 19RE

To determine

To Calculate:

The limit by using direct substitution.

Answer to Problem 19RE

The limit $\underset{x\to -1}{\lim }{e}^{-x}$ is $e$ .

Explanation of Solution

Given Information:

  $\underset{x\to -1}{\lim }{e}^{-x}$

Calculation:

A limit is the value of a function $f\left(x\right)$ when the function $f\left(x\right)$ becomes arbitory close to a unique number $L$ as $x$ approaches $c$ from the either side.

Then,

  $\underset{x\to -1}{\lim }f\left(x\right)=L$

To get the value of the limit by direction substitution,

Consider the following limit

  $\underset{x\to -1}{\lim }{e}^{-x}$

Then,

  $\begin{array}{l}\underset{x\to -1}{\lim }{e}^{-x}=e^{{\underset{x\to -1}{\lim }}^{-x}}\\ =e^{-\left(1\right)}\\ =e\end{array}$

Hence, the required limit is $\underset{x\to -1}{\lim }{e}^{-x}=e$ .