How to start with this math limit

[Petkovsky]

Homework Statement

lim 2^n/(2^n + 2)
n$$\rightarrow$$$$\infty$$

lim (1/2n) + 2n/(3n+1)
n$$\rightarrow$$$$\infty$$

Homework Equations

The Attempt at a Solution

I really have no idea where to start from so if you would like to give me some hints, I will be very pleased.

 

[Hootenanny]

A good quick tip for limiting cases is to divide both the numerator and denominator through by the highest power. So for the first one you would divide through by 2ⁿ.

 

[Petkovsky]

A good quick tip for limiting cases is to divide both the numerator and denominator through by the highest power. So for the first one you would divide through by 2ⁿ.

Thanks to that tip, I just solved the first one :).

 

[rocomath]

there are 3 things you should know about limits

1. if the higher power is in the numerator, it will go to infinity

2. if the higher power is in the denominator, it will go to zero

3. if the power in both the numerator and denominator is the same, the coefficients infront of the highest powers is the limit

 

[Gib Z]

For the quotients of polynomials that is, limits aren't always so nice for other things =]