Question

Solve:

${lim}_{x\to 0}\frac{{\sin }^3{x}^2}{x^6}$

• A. $1$
• B. $0$
• C. $-1$
• D. $\infty$

Answer 1

The correct option is A $1$

We have,

${lim}_{x\to 0}\frac{{\sin }^3{x}^2}{x^6}$

${lim}_{x\to 0}{\left(\frac{\sin x^2}{x^2}\right)}^3$

Since,

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

Therefore,

$={\left(1\right)}^3$

$=1$

Hence, this is the answer.