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Question

f(x)={|x|x, if x00, if x=0

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Solution

Here, f(x)={|x|x, if x00, if x=0

LHL = limx0 f(x) =limx0 |×|x

Putting x=0-h as x0 when x0

limh0 |0h|oh limh0 hh=1 [|-h1=h]

RHL = limx0+ f(×) =limx0+ |×|x

Putting x=0 +h x0+ ; h0

limh0 |0h|o+h limh0 hh=1

LHL / = RHL. Thus, f(×) is discontinuous at x=0.


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