A) \[\frac{3}{2\sqrt{2}}\]
B) \[\frac{1}{2\sqrt{2}}\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{6\sqrt{2}}\]
Correct Answer: D
Solution :
| \[\frac{dx}{dt}=3{{\sec }^{2}}t\] |
| \[\frac{dx}{dt}=3\sec t\tan t\] |
| \[\frac{dy}{dx}=\frac{\tan t}{\sec t}=\sin t\] |
| \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\cos t\frac{dt}{dx}\]\[=\frac{\cos t}{3{{\sec }^{2}}t}=\frac{{{\cos }^{3}}t}{3}\]\[=\,\frac{1}{3.2\sqrt{2}}=\frac{1}{6\sqrt{2}}.\] |
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