Question

Evaluate ${lim}_{x\to o}\frac{ax+sinx}{bsinx}$.

Answer 1

Consider the given function:

$f\left(x\right)={lim}_{x\to 0}\frac{ax+\sin x}{b\sin x}$

$thisis\frac{0}{0}form,soapplyllospitalrule.$

$={lim}_{a\to 0}\frac{a+(-x\sin x+\cos x)}{b\cos x}$

$=\frac{a+(0+1)}{b}$

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

Hence this is the answer.