Question

Evaluate the Given limit: \lim_{x\rightarrow 0}$$\frac{sin\,ax}{bx}

Answer 1

At x = 0, the value of the given function takes the form 0/0.
\lim_{x\rightarrow 0}$$\frac{sin\,ax}{bx}= $\lim_{x\rightarrow 0}$ $\frac{sin\,ax}{bx}$ $\times$ $\frac{ax}{bx}$
$\lim_{x\rightarrow 0}$ ($\frac{sin\,ax}{bx}$) ($\frac{a}{b}$)
$\frac{a}{b}$ $\lim_{ax\rightarrow 0}$ ($\frac{sin\,ax}{ax}$) [x$\rightarrow$0 $\Rightarrow$ ax $\rightarrow$ 0]
=$\frac{a}{b}\times 1$ [lim y$\rightarrow$0 $\frac{sin\,y}{y}$ = 1]
= $\frac{a}{b}$