Question

$\underset{x\to 0}{lim}\frac{sin2x}{{\log }_e(1+2x)}$

Answer 1

$\underset{x\to 0}{lim}\frac{sin2x}{{\log }_e(1+2x)}$

$⟹$ $\underset{x\to 0}{lim}$ $\frac{sin2x}{\left({\log }_e\right(1+2x\left)\right)}$

$⟹\underset{x\to 0}{lim}\frac{sin2x}{2x}\times \underset{x\to 0}{lim}\frac{2x}{{\log }_e(1+2x)}$

$⟹=1$