Question

The value of $\underset{x\to 0}{lim}[\frac{\tan x}{x}+\frac{\sin x}{x}]$ is

Answer 1

We know that,

$\underset{x\to 0}{lim}\frac{\tan x}{x}=1$ and $\underset{x\to 0}{lim}\frac{\sin x}{x}=1$

Hence,

$\underset{x\to 0}{lim}[\frac{\tan x}{x}+\frac{\sin x}{x}]=1+1=2$