Let f:[−π2,π2]→R be a differentiable function such that f(0)=12, If the limx→0x∫x0f(t)dtex2−1=α,then 8α2 is equal to :

Question

Let f:[−π2,π2]→R be a differentiable function such that f(0)=12, If the limx→0x∫x0f(t)dtex2−1=α,then 8α2 is equal to :
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Solution 1

The given limit is of the form 0/0, so we can apply L'Hopital's Rule.

L'Hopital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

So, we differentiate the numerator and the denominator with resp Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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