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)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

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(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

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is

For x in R , x ne0, 1, let f_(0)(x)=(1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)),n=0,1,2….. Then the value of f_(100)(3)+f_(1)((2)/(3))+f_(2)((3)/(2)) is equal to

A function f: RvecR satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n a)f^('')(x)=f(x)=0 b)4f^('')(x)+f(x)=0 c)f^('')(x)+f(x)=0 d)4f^('')(x)-f(x)=0

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot