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Question

If f(x)=xsin(1x),x0, then limx0f(x)=


A

1

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B

0

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C

-1

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D

does not exist

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Solution

The correct option is

B

0



limx0f(x)=limxsin1x,x0
LHL at x = 0 :
=limx0f(x)=limh0f(0h)
lim(h)sin(10h)
=0 as multiplication of 0 and a finite quantity is always zero.
RHL at x=0:
limh0+f(x)=limh0f(0+h)
limh0hsin(1h)=0 as multiplication of 0 and a finite quantity is always zero
limh0f(x) =limx0+f(x)
Therefore, limx0f(x)=0


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