Question

${lim}_{x\to 0}\frac{sin{x}^0}{x}$ is equal to

• A. 1
• B. $\pi$
• C. x
• D. $\frac{\pi }{180}$
  

Answer 1

The correct option is D

$\frac{\pi }{180}$

${lim}_{x\to 0}\frac{sin{x}^0}{x}$
$={lim}_{x\to 0}\frac{sin\frac{x}{180}x}{x}$
$={lim}_{x\to 0}\frac{sin\left(\frac{x}{180}x\right)}{\left(\frac{x}{180}x\right)}\times \frac{\pi }{180}$
$=lim\times 1=\frac{\pi }{180}$