Question

$\underset{x\to 0}{\lim }\frac{x\cos x+\sin x}{x^2+\tan x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{x\cos x+\sin x}{x^2+\tan x}\right] \\ \text{Dividing the numerator and the denominator by x:} \\ \underset{x\to 0}{\lim }\left[\frac{\cos x+{\displaystyle \frac{\sin x}{x}}}{x+{\displaystyle \frac{\tan x}{x}}}\right] \\ =\frac{\cos 0+1}{0+1} \\ =2 \end{gathered}$$