Question

$\underset{x\to 0}{lim}\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}$ is equal to:

• A. $\frac{\pi }{2}$
• B. $1$
• C. $\pi$
• D. $-\pi$

Answer 1

Answer: (C)

$\pi$

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

${lim}_{x\to 0}\frac{\sin \left(\pi \right(1-{\sin }^{2}x\left)\right)}{x^2}$

${lim}_{x\to 0}\frac{\sin (\pi -\pi {\sin }^{2}x)}{x^2}$

${lim}_{x\to 0}\frac{\sin \left(\pi {\sin }^{2}x\right)}{x^2}(Asx\to 0,\sin x=xandAsx\to 0,\pi {\sin }^{2}x\to 0)$

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

$=\pi$