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Question

The function |x|x2+2x,x0 and f(0)=0 is not continuous at x=0 because-

A
limx0f(x)f(0)
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B
limx0+f(x) does not exist
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C
limx0f(x) does not exist
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D
limx0f(x) does not exist.
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Solution

The correct option is C limx0f(x) does not exist.
f(x)=xx2+2xifx<0xx2+2xifx>0

f(x)=1x+2ifx<01x+2ifx>0

Clearly L.H.L =1 R.H.S =1

Hence limx0f(x) does not exist.

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