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Question

limx1xsin{x[x]}x1, where [.] denotes the greatest integer function, is

A
- 1
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B
Not existent
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C
None of these
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Solution

The correct option is B Not existent
limx1xsin{x[x]}x1RHL=limh0(1+h)sin{1+h[1+h]}1+h1=limh0(1+h)sin(1+h1)h=1LHL=limh0(1h)sin{1h[1h]}1h1=limh0(1h)sin(1h)h=LHLRHL

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