Question

Lim x tend to 0. e^x-1/10x​

Answer 1

We have:

$\lim_{x \to 0} \dfrac{e^{x}-1}{10x}$

We have to find the value of $\lim_{x \to 0} \dfrac{e^{x}-1}{10x}$.

Solution:

$\lim_{x \to 0} \dfrac{e^{x}-1}{10x}$

= $\dfrac{1}{10} \lim_{x \to 0} \dfrac{e^{x}-1}{x}$

= $\dfrac{1}{10} \times 1$ [ ∵ $\lim_{x \to 0} \dfrac{e^{x}-1}{x}=1$]

= $\dfrac{1}{10}$

∴ $\lim_{x \to 0} \dfrac{e^{x}-1}{10x}$ = $\dfrac{1}{10}$

Thus, the value of $\lim_{x \to 0} \dfrac{e^{x}-1}{10x}$ is $\dfrac{1}{10}$.