Question

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

Answer 1

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

$={lim}_{x\to 0}\frac{sin\frac{x\times \pi }{180}}{x}[\because 1^0=\frac{\pi }{180}radians]$

$={lim}_{x\to 0}\frac{sin\frac{\pi x}{180}}{x\times \frac{\pi }{180}}\times \frac{\pi }{180}$

$=\frac{\pi }{180}{lim}_{x\to 0}\frac{sin\frac{\pi x}{180}}{\frac{\pi x}{180}}$

$=\frac{\pi }{180}\times 1[\because {lim}_{x\to 0}\frac{sinx}{x}=1]$

$=\frac{\pi }{180}$