Let `g(x)=e^(f(x)) and f(x+1)=x+f(x) AA x in R`. If `n in I^(+)", then"(g'(n+(1)/(2)))/(g(n+(1)/(2)))-(g'((1)/(2)))/(g((1)/(2)))=`

Let g(x)=e^(f(x))a n df(x+1)=x+f(x)AAx in Rdot If n in I^+,t h e n(g^(prime)(n+1/2))/(g(n+1/2))-(g^(prime)(1/2))/(g(1/2))= 2(1+1/2+1/3++1/n) 2(1+1/3+1/5+1/(2n-1)) n 1

Let f(x)=[x] and g(x)=|x| . Find (f+2g)(-1)

Let g (x )=f ( x- sqrt( 1-x ^(2))) and f ' (x) =1-x ^(2) then g'(x) equal to:

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let f(x)=2x+1 and g(x)=int(f(x))/(x^(2)(x+1)^(2))dx . If 6g(2)+1=0 then g(-(1)/(2)) is equal to

Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x , then g((e^(1002) -1)/(2e^(501))) equals ...........

Suppose f and g are differentiabel functions such that xg (f(x))f'(g (x))g '(x) =f(g(x))g '(f(x)) f'(x) AA x in R and f is positive AA n in R. Also int _( 0)^(x) f (g(t )) dt =1/2 (1-e^(-2x))AA x in R, g (f(0))=1 and h (x) = (g(f (x)))/(f (g(x)))AA x in R. The graph of y =h (x) is symmetric with respect to line:

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).

Let f(x)=x^2 and g(x) = 2x + 1 be two real functions. find (f +g)(x) , (f-g)(x) , (fg)(x) , (f/g)(x) .