Question

The value of $\underset{x\to 0}{lim}\frac{e^x-e^x}{x}$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0

$\begin{array}{c}lim\left(x\to 0\right)\frac{e^x-e^x}{x}=lim\left(x\to 0\right)\frac{0}{x}\\ =\frac{0}{0}\end{array}$

applying LH rule,

$\begin{array}{c}lim\left(x\to 0\right)\frac{0}{x}=lim\left(x\to 0\right)\frac{\frac{d}{dx}\left(0\right)}{\frac{d}{dx}\left(x\right)}\\ =lim\left(x\to 0\right)\frac{0}{1}\\ =0\end{array}$

Thus option A