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  • Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 5 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 14 Inverse Trigonometric Function Exercise Fill in the Blanks Question 5 Maths Textbook Solution.

Answers (1)

Answer:

                \log_{2}e

Hint:

You must know about mean value theorem.

Given:

                f\left ( x \right )=\log_{e}x,x\: \epsilon \left [ 1,2 \right ]

Solution:

                f\left ( x \right )=\log_{e}x

On differentiating we get,

\Rightarrow {f}'\left ( x \right )=\frac{1}{x}        

\Rightarrow {f}'\left ( c \right )=\frac{1}{c}        

Apply mean value theorem,

\Rightarrow {f}'\left ( c \right )=\frac{\log_{e}2-\log_{e}1}{2-1}        

\Rightarrow \frac{1}{c}=\log_{e}2-\log_{e}1        

\Rightarrow \frac{1}{c}=\log_{e}2                                                                                                                                  \left [ \because \log_{e}1=0 \right ]

\Rightarrow \frac{1}{\log_{e}2}=c        

\Rightarrow c=\log_{2}e                                                                                                                    \left ( \because \frac{1}{\log_{e}2}=\log_{2}e \right )

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infoexpert27

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