Question

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

• A. -1
• B. 1
• C. 2
• D. -2

Answer 1

Answer: (B)

1

$\underset{x\to x}{Lim}\frac{{\int }_0^{x^2}\cos t^{2}dt}{x\sin x}=\underset{x\to x}{Lim}\frac{2x\cos x^4}{x\cos x+\sin x}$
(using L-Hospital's Rule)
$=\underset{x\to x}{Lim}\frac{2\cos x^4-8x^4\sin x^4}{2\cos x-x\sin x}=\frac{2-0}{2-0}=1$