If `f(x)={alpha+sin[x]/x , x > 0 and 2 ,x=0 and beta+[(sin x-x)/x^3] ,x < 0` (whlenotes the greatest integer function) if `f(x)` is continuous at `x = 0`. then `beta` is equal to

Let f :R-> R be defined by f(x)={(alpha+sin[x]/x,if x>0 ),(2,if x=0),(beta+[(sinx-x)/x^3],if x<0):} where [x] denotes the integral part of x. If f continuous at x = 0 , then beta-alpha =

IF f(x) =x^(2) + alpha for x ge 0 and 2 sqrt(x^(2) +1) + beta for x lt 0 is continuous at x=0 and f((1)/(2))=2, then alpha ^(2) + beta ^(2) is

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

If f (x) = (2x + 3 sin x )/(3x + 2 sin x ) , x ne 0 is continous at x = 0 then f (0) = ?

If f(x) is continuous at x=0 , where f(x)=((e^(3x)-1)sin x)/(x^(2)) , for x!=0 , then f(0)=

Let x-y sin alpha-z sin beta=0;x sin alpha-y+z sin gamma=0 and x sin beta+y sin gamma-z=0 be three planes such that alpha+beta+gamma=(pi)/(2)(alpha,beta,gamma!=0) then the planes

If f(x)=(sin(x^(2)))/(x),x!=0,f(x)=0,x=0 then at x=0,f(x) is