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Question

f(x)=tanx in 0xπ
Is Rolle's theorem applicable?

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Solution

f(x)=tanx in 0xπ
At x=π2
f(π2+)f(π2)f(π2)

f(x) is not continuous at x=π2 and not differentiable,
therefore Rolle's first two conditions are not satisfied.
Hence, Rolle's theorem is not applicable.

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