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  • Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 5 maths textbook solution

Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 5 maths textbook solution

Answers (1)

Answer:

Option (b)

Hint:

We will use the concept of Rolle’s Theorem.

Given:

\phi (x)=a^{\sin x},a> 0  and Rolle’s theorem is applicable to it.

Solution:

 \phi (x)=a^{\sin x},a> 0

Differentiate it with respect to 'x'

\phi ^{'}(x)=\log a\left ( \cos x.a^{\sin x} \right )  

\Rightarrow \; \; \phi ^{'}(c)=\log a\left ( \cos c.a^{\sin c} \right )

Let,    \phi (c)=0  

\Rightarrow \; \;\log a\left ( \cos c.\; a^{\sin c} \right )=0

\Rightarrow \; \;\cos c.\; a^{\sin c}=0

\Rightarrow \; \;\cos c=0                           

\Rightarrow \; \; \cos c=\cos \frac{\pi }{2}                                      \left [ \because \cos \frac{\pi }{2} =0\right ]

\Rightarrow \; \; c=\frac{\pi }{2}\in \left [ 0,\pi \right ]

Hence, Rolle’s Theorem is applicable in the interval \left [ 0,\pi \right ]

Option (b) is correct.

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