Answer
$\lim_{x\to0}\dfrac{\sin ax}{bx}=\dfrac{a}{b}$
Work Step by Step
$\lim_{x\to0}\dfrac{\sin ax}{bx}$ $;$ $a$ and $b$ are constants and $b\ne0$
Divide both the numerator and the denominator by $ax$:
$\lim_{x\to0}\dfrac{\sin ax}{bx}=\lim_{x\to0}\dfrac{\dfrac{\sin ax}{ax}}{\dfrac{bx}{ax}}=\lim_{x\to0}\dfrac{\dfrac{\sin ax}{ax}}{\Big(\dfrac{b}{a}\Big)}=...$
Use the quotient limit law to evaluate the limit:
$...=\dfrac{\lim_{x\to0}\dfrac{\sin ax}{ax}}{\lim_{x\to0}\dfrac{b}{a}}=\dfrac{1}{\dfrac{b}{a}}=\dfrac{a}{b}$
