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

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is

Let f (x) = { tan "" ((pi)/(4) + x)}^(1/x) , x ne 0 " and " f(0) = k . For what value of k, f(x) is

If f(x)=(x)/(1+x tan x):x in(0,(pi)/(2)), then

f(x) = (x)/(1 + x tan x), x in (0, (pi)/(2)) then a)f(x) has exactly one point of minima b)f(x) has exactly one point of maxima c)f(x) is increasing in (0, (pi)/(2)) . d)f(x) is decreasing in (0, (pi)/(2)) .

f(x)=[Tan( pi/4)+Tan x]*[Tan (pi/4)+Tan(pi/4-x)]" and "g(x)=x(x+1)" .Then the value of "g[f(x)]" is equal to "

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is