If `f'(x)=(sin2x)/(cos^(2)2x)," then "f(x)` =

If f(x)=sqrt((x-sinx)/(x+cos^2x)) , then lim_(x rarr infty)f(x) is

Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2)),"if "x gt(pi)/(2)):}" ," if f (x) is continuous at x=(pi)/(2) , find a and b .

If f(x)=(x^(2)-a^(2))/(x-a) then f(a) =

f(x)=sin^(-1)(2xsqrt(1-x^2)) then f'(x)=

If f(x)={x^2 sin((pi x)/2), |x| =1 then f(x) is

If f'(x)=(1-2sin^2x)/f(x), (f(x) ge 0, AA x in R and f(0)=1) then f(x) is a periodic function with the period

If f(x) = cos (log _(e) x), then f (x) f(y) -1/2 [f(xy) +f((x)/(y))] has the value-

If f(x) =1/2 ( sin x+ cos x) + ce ^(-x), then the vlaue of [f ' (x)+ f(x) ] is=

f(x) = sin^-1 frac(2x)(1+x^2) then