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Question

lf a function f(x) is defined as f(x)={xx2,x00x=0 then

A
f(x) is continuous at x=0 but not differentiable at x=0
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B
f(x) is continuous as well as differentiable at x=0
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C
f(x) is discontinuous at x=0
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D
f(x) is continuous everywhere
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Solution

The correct option is A f(x) is discontinuous at x=0
f(x)=xx2;x00;x=0
f(x)=x±xx0
if x>0f(x)=xx=1
if x<0f(x)=xx=1
limx0+f(x)=1
limx0f(x)=1
LHLRHL Discontinuous at x=0

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