If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for ...

If `f(x)=(e^(x)+e^(-x)-2)/(x sin x)`, for `x in [(-pi)/(2), (pi)/(2)]-{0}`, then for f to be continuous in `[(-pi)/(2), (pi)/(2)], f(0)=`

A

(a) 0

B

(b) 1

C

(c) `e`

D

(d) `e^2`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2] . If f(x) is continuous in [0,(pi)/2] , then f((pi)/(4)) is

If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

If f(x) = (tan(pi/4-x))/(cot2x), x != pi/4 , is continuous in (0, pi/2) , then f((pi)/(4)) is equal to

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)^2),w h e nx!=pi/2a n df(pi/2)=lambda, the f(x) will be continuous function at x=pi/2,w h e r elambda=

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

If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0 , then the value of f(0) so that f is continuous at x = 0 is

Let f(x) = log (sin x+ cos x) , x in (-pi/4,(3pi)/(4)) Then f is stricly increasing in the interval