Q. 17 - Calculus

Question

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive.

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

Step-by-Step Solution

Answer

The value of the limit is $\underset{x\to 0}{\lim }\frac{e^x-1}{x}=1.$

Step 1. Given Information.

The given limit function is $\underset{x\to 0}{\lim }\frac{e^x-1}{x}.$

Step 2. Filling the blank.

To find the value of the limit applies L'Hopital's rule.

So,

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

Now, put the value $x=0$

$$\begin{gathered} =\frac{e^0}{1} \\ =1 \end{gathered}$$