Question

${lim}_{x\to 0}\frac{sin3x+7x}{4x+sin2x}$

Answer 1

${lim}_{x\to 0}\frac{sin3x+7x}{4x+sin2x}$

$={lim}_{x\to 0}\frac{(\frac{sin3x}{x}+\frac{7x}{x})}{(\frac{4x}{x}+\frac{sin2x}{x})}=\frac{({lim}_{x\to 0}\frac{sin3x}{3x}\times 3)+7}{4+\left({lim}_{x\to 0}\frac{sin2x}{2x}\right)\times 2}$

$=\frac{3+7}{4+2}=\frac{10}{6}=\frac{5}{3}$