Let ` f ` be a continuous function on `R` such that `f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1)` Then the value of `f(0) ` is

Let f be a continuous function on R such that f(1//2^n) =(sin e^n) e^(-n^2)+(2n^2)/(n^2+1) .Then the value of f(0) is

Let f be a function from be set of positive integers to the set of real numbers i.e. f: N to R , such that f(1)+2f(2)+3f(3)+……+nf(n)=n(n+1)f(n) form ge2 , then find the value of f(1994).

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

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is:

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is:

Let f be a function from the set of positive integers to the set of real number i.e f : N rarr R , such that f(1) = 1 and r=1 to n ∑ ​ rf(r)=n(n+1)f(n),∀n≥2' then the value of 2126f(1063)

If a function F is such that F(0)=2 , F(1)=3 , F(n+2)=2F(n)-F(n+1) for n ge 0 , then F(5) is equal to

If a function F is such that F(0)=2 , F(1)=3 , F(n+2)=2F(n)-F(n+1) for n ge 0 , then F(5) is equal to

Let f(x) be a real valued function not identically zero such that f(x+y^(2n+1))=f(x)+(f(y))^(2n+1), n epsilon N and x, y epsilo R . If f'(0)ge0 , then f'(6) is