Question

Find limit
$\underset{x\to 0}{lim}\frac{\sin 2x+3x}{2x+\sin 3x}$

Answer 1

${lim}_{x\to 0}\frac{sin2x+3x}{2x+sin3x}$

on using L'Hosptal rule we have

${lim}_{x\to 0}\frac{2cos2x+3}{2+3cos3x}$

using limit

$\frac{2\times 1+3}{2+3\times 1}$ = \frac{5}{5} = 1