limx→1xsin{x−[x]}x−1, 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 limx→1xsin{x−[x]}x−1RHL=limh→0(1+h)sin{1+h−[1+h]}1+h−1=limh→0(1+h)sin(1+h−1)h=1LHL=limh→0(1−h)sin{1−h−[1−h]}1−h−1=limh→0(1−h)sin(1−h)−h=∞LHL≠RHL