How to start with this math limit

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To solve the limit of 2^n/(2^n + 2) as n approaches infinity, divide both the numerator and denominator by 2^n, leading to a limit of 1. For the second limit (1/2n) + 2n/(3n+1), applying the same technique reveals that the limit approaches 2/3 as n approaches infinity. Key principles for evaluating limits include recognizing that if the higher power is in the numerator, the limit goes to infinity, while if it’s in the denominator, it approaches zero. When the powers are equal, the limit is determined by the coefficients of the highest powers. Understanding these concepts is crucial for tackling polynomial limits effectively.
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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.
 
Last edited:
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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.
 
Hootenanny said:
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 :).
 
Last edited:
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
 
For the quotients of polynomials that is, limits aren't always so nice for other things =]
 

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