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Question

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

A
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B
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C
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D
does not exist
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Solution

The correct option is D does not exist
The given function can be restated as
f(x)=sin[x][x]ifxϵ(,0)[1,]0ifxϵ[0,1)
limx0f(x)=limh0sin[h][h]
=limh0sin(1)(1)=sin1 and limx0+f(x)=limh00=0
limx0+f(x)limx0+f(x)
limx0f(x) does not exist

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