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  • need solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise multiple choice question 11

need solution for rd sharma maths class 12 chapter 14 Mean Value Theoram exercise multiple choice question 11

Answers (1)

Answer:

Option (b)

Hint:

You must know about the concept of Rolle’s Theorem.

Given:

f(x)=e^{x}\sin x,x\in \left [ 0,\pi \right ]

Solution:

        f(x)=e^{x}\sin x

\Rightarrow f^{'}(x)=e^{x}\cos x-\sin x\left ( e^{x} \right )

\Rightarrow f^{'}(x)=e^{x}(\cos x -\sin x )

\Rightarrow f^{'}(c)=e^{c}(\cos c -\sin c )

As Rolle’s Theorem,

\Rightarrow f^{'}(c)=0

\Rightarrow e^{c}(\cos c -\sin c )=0

\Rightarrow \cos c -\sin c =0

\Rightarrow \cos c=\sin c

\Rightarrow \sin \left ( \frac{\pi }{2}-c \right )=\sin c

\Rightarrow c=\frac{\pi }{2}-c

\Rightarrow 2c=\frac{\pi }{2}

\Rightarrow c=\frac{\pi }{4}

Option (b) is correct.

 

 

Posted by

infoexpert26

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