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) \[ta{{n}^{-1}}2\]                    

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

Correct Answer: B

Solution :

\[y=2{{e}^{2x}}\]	?(i)
\[\therefore \]      \[\frac{dy}{dx}=2\cdot {{e}^{2x}}\cdot 2=4\cdot {{e}^{2x}}\]

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

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

\[\therefore \]      required angle\[=\text{90}-\theta \]

\[\Rightarrow \]   \[\frac{\pi }{2}-{{\tan }^{-1}}4\]           =         \[{{\cot }^{-1}}4\]