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If f(x)=[{:(mx+1,if x le (pi)/(2)),(sin...

If `f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):}` is continuous at `x = (pi)/(2)`, then

A

`m=1, n=0`

B

`m=(m pi)/(2)+1`

C

`n=m(pi)/(2)`

D

`m=n=(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, f(x) is continuous at `x=(pi)/(2)`
`lim_(x to (pi^(-))/(2)) (mx+1)=lim_(x to (pi^(+))/(2))(sinx+n)`
`rArr m(pi)/(2)+1="sin"(pi)/(2)+n`
`therefore (m pi)/(2)=n`
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