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Question

Match the entries in List I with entries in List II

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Solution

Element A:
f(x)=tanx+cotx2tanxcotx2
f(x)={cotx,tanxcotxtanx,tanx<cotx
There are 4 points (π4,3π4,5π4,7π4) where the above function is continuous but not differentiable in (0,2π)
Element B:
f(x)=min{1,1+x3,x23x+3}
f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪1+x3,x01,0<x1x23x+3,1<x21,x>2
f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪3x2,x00,0<x12x3,1<x21,x>2
There are 2 point x=1 and x=2 where the above function is not differentiable.
Element C:
f(x)=(x+4)1/3
f(x)=13(x+4)2/3
Not derivable at x=4
Element D:
f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪π2ln(x.2π)+π2,0<xπ2πx,π2<x<3π2
f(x)=⎪ ⎪⎪ ⎪π2x0<x<π21π2<x<3π2
f(π2)=f(π+2)=1
function differentiable at x=π2

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