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If [x] denotes the integeral part of x a...

If [x] denotes the integeral part of x and in `(0,pi),` we define
`f (x) {{:([ (2 (sin x - sin ^(n) ) + | sin x - sin ^(n) x | )/(2 (sin x - sin ^(n) x) - | sin x - sin ^(n) x|)] ,x ne (pi)/(2)), (" "3, x = (pi)/(2)):}`Then for `n gt 1`

A

f (x) is continuous but not differentiable at `x = (pi)/(2)`

B

both continuous and differentiable at `x = (pi)/(2)`

C

neither continuous nor differentiable at `x = (pi)/(2)`

D

`lim _(xto (pi)/(2)) f (x)` exists but `lim _( x to (pi)/(2)) f (x) ne f ((pi)/(2))`

Text Solution

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The correct Answer is:
B
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NTA MOCK TESTS-NTA TPC JEE MAIN TEST 79-MATHEMATICS
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