Q.

If  f(x)=sin[x][x], for [x]00, for [x]=0 where [x] denotes the greatest integer less than or equal to x, then limx0f(x)

 

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a

does not exist

b

1

c

-1

d

0

answer is D.

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Detailed Solution

The given funciton is 

f(x)=sin[x][x], if x(,0)[1,)0, if x[0,1)

limx0-f(x)=limh0-sin[h][h]

=sin(1)(1)=sin1 limx0+f(x)=sin(0)(0)=0

limx0-f(x)limx0+f(x).

therefore, limx0f(x) does not exist.

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