If `f(x)={(tan[x^2]pi)/(a x^2)+a x^3+b ,0 < x <= 1 2 cos pi x + tan ^-1 x, 1 < x < 2` is differentiable in (0,2) and if `a=1/k_1 and b= pi/4- 26/k_2,` then the value of `(k_1^2+k_2^2)/20` is

the function f(x)=(6/5)^((tan6x)/(tan5x)) if x is 0 to pi/2 and f(x)=b+2 if x=pi/2 and f(x)=(1+|cosx|)^{(a*|tanx|)/b} if x is pi/2 to pi Determine the values of a&b. if f is continuous at x=pi/2

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

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

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

if f(x) = {:{ (1+x, ,0 le x le2), (3-x, ,2 lt x le3):} Determine the points of discontinuity of the function f (f(x)) (ii) Check the continuity of the function f(x) = [x]^(2) - [x^(2)] (iii) find the values of a and b if f is continuous at x = pi/2 f(x)= {:{((8/5)""^(tan8x)/(tan 5x) , , 0 lt x lt pi//2),(a+4, , x=pi//2), ((1+|cot x|)""^(b|tan x|)/a, , pi/2 lt x lt pi):}

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

If f(x)={sin((a-x)/(2))tan[(pi x)/(2a)] for x>a and ([cos((pi x)/(2a))])/(a-x) for x

The function f(x) = [{:((6/5)^(tan 6x)/(tan 5x), if, 0 lt x lt pi/2),(b+2, if, x = pi/2),((1+|cos x|)^((a|tan x|)/b),f if, pi/2 lt x lt pi):} Determine the values of 'a' & 'b', if f is continous at x = pi//2 .