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Question

The value of limx0[sin[x3][x3]] is
(where [.] represents the greatest integer function)

A
0
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B
1
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C
sin1
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D
does not exist
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Solution

The correct option is D does not exist
L.H.L.=limx0[sin[x3][x3]]
=limh0[sin([0h3])[0h3]]
=limh0[sin([h3])[h3]]
=[sin(4)4]
=[sin(4)4]=1
(sin4<0 as π<4<3π2)

R.H.L.=limx0+[sin([x3])[x3]]
=limh0[sin([0+h3])[0+h3]]
=[sin(3)3]
=[sin(3)3]=0
(sin3>0 as π2<3<π)

L.H.L.R.H.L.
Hence, limit does not exist.

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