Value of this function as n approaches infinity

[michonamona]

Homework Statement

f(x) = lim $$_{n->\infty}$$(x$${n}$$)/(1+x$${n}$$)

Homework Equations

Suppose that x=1

The Attempt at a Solution

Wouldnt f(x) = 1/2? Because 1^n = 1, so the denominator is 2. The solution says that f(x)=1. Why is that?

 

[kmikias]

Hi
yes the answer is f(x)=1 because both of them have the highest power of n so based on that if you have the same power you just take the cofficient which is one.
x^n/x^n = 1 when the limit goes to infinity.

 

[LCKurtz]

Yes f(1) is 1/2. The limit is 1 if x > 1 and 0 for x between 0 and 1.