If f(x) is continuous and differerntiable function such that `f((1)/(n))=0` for all `n in N`, then

Let f:NrarrN in such that f(n+1)gtf(f(n)) for all n in N then

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in [0,1]forw h i c hf^(prime)(c)(f(c))^(n-1)>sqrt(2^(n-1)) , where n in Ndot

A function f:R to R is differernitable and satisfies the equation f((1)/(n)) =0 for all integers n ge 1 , then

Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x))=1 for all x in[0,1] then:

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(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if (f(x))^(2)=1, forall x in [0,n], then number of functions f(x) are

The funciton f: N to N given by f(n)=n-(-1)^(n) for all n in N is

Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. (b) f(x) is everywhere continuous but not differentiable at x=n\ pi,\ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)pi/2 , n in Z . (d) none of these

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

If f(x) is a real valued functions satisfying f(x+y) = f(x) +f(y) -yx -1 for all x, y in R such that f(1)=1 then the number of solutions of f(n) = n,n in N , is