Question

$\underset{x\to 0}{lim}\frac{2+2x+sin2x}{(2x+sin2x)e^{sinx}}$ is:

• A. equal to zero
• B. equal to $1$
• C. equal to $-1$
• D. non existent

Answer 1

The correct option is D non existent

${lim}_{x\to 0}\frac{2+2x+\sin 2x}{(2x+\sin 2x)e^{\sin x}}$

$={lim}_{x\to 0}(\frac{1}{e^{\sin x}}+\frac{2}{(2x+\sin 2x)e^{\sin x}})$

$=1+\frac{2}{0\times 1}=\infty \Rightarrow$ not defined