`lim_(x rarr oo) (1+f(x))^(1/f(x))`

If f(x)=e^(x), then lim_(x rarr oo)f(f(x))^((1)/()(x)})); is equal to (where {x} denotes fractional part of x).

lim_(x rarr oo)(x-1)/(x)

f(x)=e^x then lim_(x rarr 0) f(f(x))^(1/{f(x)} is

lim_(x rarr oo)(x)/(x+1)

Let f:R rarr R be a positive increasing function with lim_(x rarr oo)(f(3x))/(f(x))=1 then lim_(x rarr oo)(f(2x))/(f(x))=

Let f:rarr R rarr(0,oo) be strictly increasing function such that lim_(x rarr oo)(f(7x))/(f(x))=1 .Then, the value of lim_(x rarr oo)[(f(5x))/(f(x))-1] is equal to

Let f:R rarr R be a positive increasing function with lim_(x rarr oo)(f(3x))/(f(x))=1. Then lim_(x rarr oo)(f(2x))/(f(x))=(1)(2)/(3)(2)(3)/(2)(3)3(4)1

f(a)=2,f'(a)=1,g(a)=-1,g'(a)=-2 then lim_(x rarr oo)(g(x)f(a)-g(a)f(x))/(x-a), is

Statement 1: lim_ (x rarr oo) ((1 ^ (2)) / (x ^ (3)) + (2 ^ (2)) / (x ^ (3)) + (3 ^ (2)) / (x ^ (3)) + ...... + (x ^ (2)) / (x ^ (3))) = lim_ (x rarr oo) (1 ^ (2)) / (x ^ ( 3)) + lim_ (x rarr oo) (2 ^ (2)) / (x ^ (3)) + ...... + lim_ (x rarr a) (x ^ (2)) / (x ^ (3)) lim_ (x rarr a) (f_ (1) (x) + f_ (2) (x) + ... + f_ (n) (x)) = lim_ (x rarr a) f_ (1) (x) + lim_ (x rarr a) f (x) + ...... + lim_ (x rarr a) f_ (n) (x)