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Question

Evaluate: limx0ddx(1-cosx)x2dx


A

1

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B

0

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C

12

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D

None of these

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Solution

The correct option is C

12


Explanation for the correct answer:

Simplifying the equation to determinate form and applying the limits:

limx0ddx(1-cosx)x2dxlimx0(1-cosx)x2[Differntiationandintegrationgetscancelled]limx0-(-sinx)2xddx(1-cosx)x2=-(-sinx)2x

Applying the limits

12×1limx0sinθθ=112

Thus, limx0ddx(1-cosx)x2dx=12

Therefore, the correct answer is option (C).


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