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Question

Let f(x)=1|cosx| xR, then which among the following options is/are correct?

A
f(π2) does not exist
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B
f(x) is continuous everywhere
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C
f(x) is not differentiable everywhere
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D
limxπ2+f(x)=1
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Solution

The correct option is D limxπ2+f(x)=1

f(x)=1|cosx| is continuous as cosx is continuous for all x which gives |cosx| is also continuous.
Hence, 1|cosx| is continuous.

Also, limxπ2+f(x)=limxπ2+1|cosx|=1

Also, since f(x) has sharp corner at x=π2. Hence, f(π2) does not exist.

Similar sharp corners occur at all the points where cosx=0 i.e. at x=(2n+1)π2,nZ.
Hence, f(x) is not differentiable everywhere.

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