Question

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

Answer 1

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

$={lim}_{x\to 0}\frac{1}{\frac{sin{x}^2}{x^2}}$

$=\frac{1}{{lim}_{x\to 0}\frac{sin{x}^2}{x^2}}[\because {lim}_{x\to 0}\frac{sinx}{x}=1]$

$=\frac{1}{1}=1$