Question

${lim}_{x\to 0}\frac{ax+xcosx}{bsinx}$

Answer 1

${lim}_{x\to 0}\frac{ax+xcosx}{bsinx}$

$={lim}_{x\to 0}\frac{\frac{a+cosx}{bsinx}}{x}=\frac{li{m}_{x\to 0}a+li{m}_{x\to 0}cosx}{li{m}_{x\to 0}\frac{bsinx}{x}}$

$=\frac{a+1}{b}[\because {lim}_{\theta \to 0}\frac{sin\theta }{\theta }=1]$

$=\frac{a+1}{b}$