Home
Class 12
MATHS
If f(x) = {(ax+1,",",x le (pi)/(2)),(sin...

If `f(x) = {(ax+1,",",x le (pi)/(2)),(sin x+ b,",",x gt (pi)/(2)):}` is continuous at `x = (pi)/2`, then

A

(a) `a = 1, b =0`

B

(b) `a = b(pi)/2+1`

C

(c) `b = (api)/2`

D

(d) `a = b = (pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi)/(2)),(3",", "if " x =(pi)/(2)):} is continuous at x=(pi)/(2) then k?

If f(x) = {((1-sinx)/(pi-2x), ",", x != pi/2),(lambda, ",", x = pi/2):} , be continuous at x = (pi)/2 , then the value of lambda is

If f(x) ={((3sinx-sqrt(3)cosx)/(6x-pi),",",x != (pi)/6),(a, ",",x = pi/6):} is continuous at x = (pi)/6 , then a =

If {:(f(x),=(cos x - sin x)/(cos 2x),",", x != (pi)/4),(,=k, ",", x = (pi)/4):} is continous at x = (pi)/4 , then the value of k is

If f(x) = {(2x+1,",",x le 1),(-3-kx^(2),",",x gt 1):} is continuous at x = 1, then the value of k is

If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x = 2, then the value of k is

If f(x) is continuous over [-pi, pi] , where f(x) is defined as f(x) = {(-2sin x, ",",-pi le x le (-pi)/2),(alpha sin x + beta, ",", -(pi)/2 lt x lt (pi)/2 ),(cos x, ",", (pi)/2 le x lt pi ):} then alpha and beta equals

f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(pi)/(2)):} at x =(pi)/(2) is

Let f(x) = {(-2sin x, ",","if" x le -(pi)/2),(A sin x + B, ",", "if"-(pi)/2 lt x lt (pi)/2 ),(cos x, ",", "if" x ge (pi)/2 ):} Then