If `f (x)` be a differentiable function satisfying `f (y) f ((x)/(y))=f (x) AA, x y in R, y ne 0 and f (1) ne 0,f (1) =3,` then

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(y)+f(y)/(x) AAx, y in R ^(+) also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))] (where [.] denotes greatest integer function).

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) = alpha e^(beta) . Then, |alpha + beta| is equal to.......

Let f be a differentiable function satisfying the condition f ((x)/(y)) = (f(x))/(f (y)) (y ne 0, f (y) ne 0) AA x, y in R and f '(1) =2. If the smaller area enclosed by y = f(x) , x ^(2)+y^(2) =2 is A, then findal [A], where [.] represents the greatest integer function.

Let be a real function satisfying f(x)+f(y)=f((x+y)/(1-xy)) for all x ,y in R and xy ne1 . Then f(x) is

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

If f:R rarr (0,oo) be a differentiable function f(x) satisfying f(x+y)-f(x-y)=f(x)*{f(y)-f(-y)}, AA x, y in R, (f(y)!= f(-y) " for all " y in R) and f'(0)=2010 . Now, answer the following questions. Which of the following is true for f(x)

If f:R rarr (0,oo) be a differentiable function f(x) satisfying f(x+y)-f(x-y)=f(x)*{f(y)-f(y)-y}, AA x, y in R, (f(y)!= f(-y) " for all " y in R) and f'(0)=2010 . Now, answer the following questions. let g(x)=log_(e)(sin x) , and int f(g(x))cos x dx=h(x)+c , (where c is constant of integration), then h(pi/2) is equal to

Let f be a differential function satisfying the condition. f((x)/(y))=(f(x))/(f(y))"for all "x,y ( ne 0) in R"and f(y) ne 0 If f'(1)=2 , then f'(x) is equal to