If `f(x)=(1+x)^n,` then the value of `f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot`

If f(x + y) = f(x) +f(y), then the value of f(0)

If f''(0)=k,kne0 , then the value of lim_(xto0)(2f(x)-3f(2x)+f(4x))/(x^2) is

If f''(0)=k,kne0 then the value of lim_(xrarr0)(2f(x)-3f(2x)+f(4x))/(x^(2)) is

if f(x)=mx+c and f(0)=f'(0)=1 then find the value of f(3)

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)

If y=f{f(x)} , f(0) =0 and f'(0)=5, then the value of [(dy)/(dx)]_(x=0) is-

If f(x)=(a^x)/(a^x+sqrt(a ,)),(a >0), then find the value of sum_(r=1)^(2n-1)2f(r/(2n))

If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(0)=0, then the value of |2/(f(2))| is___

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4