question_answer

The angle at which the curve \[y=2{{e}^{2x}}\] intersects the y-axis is -

A) \[{{\tan }^{-1}}4\]

B) \[{{\cot }^{-1}}4\]

C) \[{{\tan }^{-1}}2\]

D) \[{{\cot }^{-1}}2\]

Correct Answer: B

Solution :

\[y=2{{e}^{2x}}\]                               ...(i)

\[\therefore \,\,\,\,\frac{dy}{dx}=2.\,\,{{e}^{2x}}.2=4.\,\,{{e}^{2x}}\]

\[\therefore \,\,\,\,\left( \frac{dy}{dx} \right)at\,\,P=4\]

\[\therefore \,\,\,\,\tan \theta =4\]  \[\Rightarrow \theta ={{\tan }^{-1}}4\]

\[\therefore \]  required angle \[=90-\theta =\frac{\pi }{2}-{{\tan }^{-1}}4\]

\[={{\cot }^{-1}}4\]