Question

Solve ${lim}_{x\to 0}\frac{\sin x}{\sqrt{x^2}}$

• A. $1$
• B. $-1$
• C. $0$
• D. doesn't exist

Answer 1

The correct option is A $1$

According to question,

$li{m}_{x\to 0}\frac{sinx}{\sqrt{x^2}}$

$⟹li{m}_{x\to 0}\frac{sinx}{x}$

Using expansion of $sinx$,

$⟹li{m}_{x\to 0}\frac{x-\frac{x^3}{3!}+\frac{x^5}{5!}-........}{x}$

$⟹li{m}_{x\to 0}1-\frac{x^2}{3!}+\frac{x^4}{5!}-........$

Now putting $x=0$, we get

$⟹1$