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Question

Discuss the continuity and differentiabilty of f(x)=|log|x||.

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Solution

f(x)=|log|x|||x|0
i.e at x=0,f(x) is discontinuous
Let t=log|x|
f(x)=|t| which is not differentiable at t=0log|x|=0|x|=1x=±1
f(x) is not differentiable at x=0,1,1

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