(A) 2 f(r and (2) 1, then lim f(r) is: -I (B) 1

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

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 ( x) = Sigma_(r=1)^(n) tan^(-1) ( 1/(x^(2) + ( 2r -1) x + (r^(2) - r + 1)))" , then " | lim_(n to oo) f'(0)| is

If f ( x) = Sigma_(r=1)^(n) tan^(-1) ( 1/(x^(2) + ( 2r -1) x + (r^(2) - r + 1)))" , then " | lim_(n to oo) f'(0)| is

If f ( x) = Sigma_(r=1)^(n) tan^(-1) ( 1/(x^(2) + ( 2r -1) x + (r^(2) - r + 1)))" , then " | lim_(n to oo) f'(0)| is

Let f: R rarr R be a function such that f(2)=4 and f'(2)=1 . Then, the value of lim_(x rarr 2) (x^(2)f(2)-4f(x))/(x-2) is equal to

If f(r)=1+(1)/(2)+(1)/(3)+.......(1)/(r) and f(0)=0, then sum_(r=1)^(n)(2r+1)f(r)

If f:R rarr R is continous function satisying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to