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`

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

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

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 a. 0 b. -log2 c. 1 d. e

If f:R rarr R be a differen tiable function atg x=0 satisfying f(0)=0 and f'(0)=1 then the value of lim_(x rarr0)(1)/(x)sum_(n=1)^(oo)(-1)^(n)f((x)/(n))=e b.-log2 c.0 d.1

Let f:R rarr R be differentiable at x = 0. If f(0) = 0 and f'(0)=2 , then the value of lim_(xrarr0)(1)/(x)[f(x)+f(2x)+f(3x)+….+f(2015x)] is

Let f is twice differerntiable on R such that f (0)=1, f'(0) =0 and f''(0) =-1, then for a in R, lim _(xtooo) (f((a)/(sqrtx)))^(x)=

Let f is twice differerntiable on R such that f (0)=1, f'(0) =0 and f''(0) =-1, then for a in R, lim _(xtooo) (f((a)/(sqrtx)))^(x)=

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 :

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then lim_(x->0)(f(x)-1)/x is a. 1//2 b. 1 c. 2 d. 0