Question

$\underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}$ equals

• A. $\frac{a}{b}$
• B. $ab$
• C. $\frac{b}{a}$
• D. 1

Answer 1

The correct option is A $\frac{a}{b}$

$\underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}=\underset{x\to 0}{lim}\frac{\frac{a\sin ax}{ax}}{\frac{b\sin bx}{bx}}=\frac{\underset{x\to 0}{lim}\frac{a\sin ax}{ax}}{\underset{x\to 0}{lim}\frac{b\sin bx}{bx}}=\frac{a}{b}$