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If f (x)= {{:((sin {cos x})/(x- (pi)/(2)...

If `f (x)= {{:((sin {cos x})/(x- (pi)/(2)) , x ne (pi)/(2)),(1, x= (pi)/(2)):},` where {k} represents the fractional park of k, then:

A

f (x) is continous at `x = (pi)/(2)`

B

`lim _(x to (pi)/2)` f (x) does not exist

C

`lim _(x to (pi)/(2))f (x)` exists, but f is not continuous at `x = (pi)/(2)`

D

`lim _(x to (pi)/(2))f (x)=1`

Text Solution

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The correct Answer is:
B
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