If `lm_(x->oo) f(x)` exists and is finite and nonzero and if `lim_(x->oo) {{f(x)+(3f(x)−1)/(f_2(x))}=3`,then the value of `lim_(x->oo) f(x)` is

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

If f(x)=x(-1)^[1/x] xle0 , then the value of lim_(xto0)f(x) is equal to

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

If lim_(xtoa) {(f(x))/(g(x))} exists, then

lim_(x to oo) (sinx)/x is …….

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

Let f(a)=g(a)=k and their nth derivatives exist and be not equal for some n. If lim_(xtoa) (f(a)g(x)-f(a)-g(a)f(x)+g(a))/(g(x)-f(x))=4 then find the value of k.

Evaluate: lim_(x->oo) root(3)((x+1)(x+2)(x+3))-x