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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 continuous at `x=pi//2`

B

`lim_(xrarrpi//2)f(x)` exists, but f is not continuous at `x=pi//2`

C

`lim_(xrarrpi//2)f(x)` does not exist

D

`lim_(xrarrpi//2)f(x)=-1`

Text Solution

Verified by Experts

The correct Answer is:
C
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