If `f(x) = (tan x cot alpha)^(1/(x-alpha)), x != alpha` is continuous at `x=alpha`, then the value of `f(alpha)` is-

If cos x -sin alpha cot beta sin x=cos alpha then the value of tan x/2 is

lim_(x rarr alpha)(tan x cot alpha)^((1)/(x-a)) is equal to

If cos x-sin alpha cot beta sin x=cos alpha , then the value of tan (x//2) is

If cos x - sin alpha cot beta sin x = cos alpha then the value of tan(x//2) is

If lim_(x to alpha) (alpha^x - x^alpha)/(x^alpha - alpha^alpha) = -1 then what is the value of alpha ?

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

If f(x) = x^2 - 3x + 1 and f (2 alpha) = 2 x f(alpha) =