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Question

The function f(x)=|x3|x3 at x=3, is

A
Left continuous
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B
Right continuous
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C
continuous
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D
discontinuous
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Solution

The correct option is D discontinuous
we just concentrate on the function |x|x
LHL = lim x0|x|x=xx=1

RHL = lim x0+|x|x=xx=1

Let , y=x3
Now, if x3,then ,y0
Applying the above derived result for y,
Since, the LHL is not equal to the RHL,
Hence the function is discontinuous at y = 0 or x = 3

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