Question

$\underset{x\to 0}{lim}\frac{in{t}_0^{x^2}\cos t^{2}dt}{x\sin x}$ is equal to

• A. $1$
• B. $2$
• C. $0$
• D. none of these

Answer 1

The correct option is A $1$

${lim}_{x\to 0}\frac{{\int }_0^{x^2}\cos t^{2}dt}{x\sin x}$

U\sin g L'Hospital rule, we get

$={lim}_{x\to 0}\frac{\cos \left(x^2\right)\times 2x}{\sin x+x\cos x}$

Again Using L'Hospital rule, we get

$={lim}_{x\to 0}\frac{\cos \left(x^2\right)\times 2}{\sin x/x+\cos x}=1$

Hence, option 'A' is correct.