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)^(n) , then the value of f(0)+f'(0)+(f''(0))/(2!)+...+(f^(n)(0))/(n!) , is

If f(x)=(2011 + x)^(n) , where x is a real variable and n is a positive interger, then value of f(0)+f'(0)+ (f'' (0))/(2!)+...+ (f^((n-1))(0))/((n-1)!) is -f(0)+f'(0)+ (f'' (0))/(2!)+...+ (f^((n-1))(0))/((n-1)!) is -

If f : R to R is given f (x) = x +1, then the value of lim _( b - oo) (1)/(n) [ f (0) + f ((5)/(n)) + f ((10)/(n)) +...+ f ((5 ( n -1))/( n )) ], is :

a_(0)f^(n)(x)+a_(1)f^(n-1)(x)*g(x)+a_(2)f^(n-2)g^(2)(x)+......+a_(n)g^(n)(x)>=0

If f(0)=0,f'(0)=2 then the derivative of y=f(f(f(x))) at x=0 is

Let f:R to R differerntiable at x=0 and satisfies f(0)=0 and f'(0)=1, then the value of lim_(x to 0) (1)/(x) sum_(x to 1)^(oo) (-1)^(n) f((x)/(n))is