$\"\"$

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The function is $\"\"$ .

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The function satisfy the mean value theorem over the interval $\"\"$ .

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Find the values of $\"\"$ , $\"\"$ and $\"\"$ .

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Mean value Theorem :

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If $\"\"$ is continuous on $\"\"$ and differentiable on open interval $\"\"$ , then there exists a number $\"\"$ in $\"\"$ such that $\"\"$ .

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$\"\"$

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The function is continuous as it satisfies the mean value theorem.

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Consider $\"\"$ .

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Find the limit as $\"\"$ tends to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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The function approaches to $\"\"$ as $\"\"$ tends to $\"\"$ .

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So $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Find the limit as $\"\"$ tends to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Since the the function is continuous at $\"\"$ , $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Find the limit as $\"\"$ tends to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Since the the function is continuous at $\"\"$ , $\"\"$ .

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$\"\"$

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$\"\"$

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The function is differentiable as it satisfies the mean value theorem.

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Consider $\"\"$ .

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Apply derivative with respect to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply derivative with respect to $\"\"$ .

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$\"\"$

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Since the the function is differentiable at $\"\"$ , $\"\"$ .

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Substitute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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Therefore the values are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .