Question

$ \underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi {{\cos }^{2}}x)}{{{x}^{2}}} $ equals to

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

Answer 1

Answer: (B)

The equation of normal at $ \left( ct,\frac{c}{t} \right) $ on the curve $ xy={{c}^{2}} $ is $ ty={{t}^{3}}x-c{{t}^{4}}+c $ If it passes through $ \left( ct,\frac{c}{t} \right) $ then $ t\frac{c}{t}={{t}^{3}}.ct-c{{t}^{4}}+c $ $ \Rightarrow $ $ t={{t}^{3}}t{{}^{2}}-{{t}^{4}}t+t $ $ \Rightarrow $ $ t-t={{t}^{3}}t(t-t) $ $ \Rightarrow $ $ 1=-{{t}^{3}}t $ $ \Rightarrow $ $ t=-\frac{1}{{{t}^{3}}} $