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Question

limx1xsin{x}x1, where {x} denotes the fractional part of x, is equal to

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 D does not exist

limx10{x}=limx10(x[x]) = 1-0=1
limx1+0{x}=limx1+0(x[x]) = 1-1=0
limx10xsin{x}x1=limx10sin{x}=
limx1+0xsin{x}{x}x1x1=1×1×1=1
Since, L.H. limit R.H. limit Limit does not exist.

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