Question

Evaluate $\underset{x\to 0}{lim}\frac{sinax}{bx}$

• A. d
• B. b
• C.
• D.

Answer 1

The correct option is C

We have, $\underset{x\to 0}{lim}\frac{sinax}{bx}$

At x-0, the value of the given function takes the form $\frac{0}{0}$

Now, $\underset{x\to 0}{lim}\frac{sinax}{bx}$

Multiplying ax in both numerator and denominator

$\underset{x\to 0}{lim}\frac{sinax}{ax}\times \frac{ax}{bx}$

$\underset{x\to 0}{lim}\left(\frac{sinax}{ax}\right)\times \left(\frac{ax}{bx}\right)$

$=\left(\frac{a}{b}\right)\underset{x\to 0}{lim}\left(\frac{sinax}{ax}\right)$ $[x\to 0\Rightarrow ax\to 0]$

$=\frac{a}{b}\times 1\{\underset{x\to 0}{lim}\frac{sinx}{x}=1\}$

$=\frac{a}{b}$

Answer option C is correct