How to start with this math limit

  • Thread starter Thread starter Petkovsky
  • Start date Start date
  • Tags Tags
    Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating limits in calculus, specifically focusing on two limit expressions as n approaches infinity. Participants are exploring methods to approach these limits and discussing the implications of polynomial degrees in the context of limits.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the strategy of dividing by the highest power in the numerator and denominator to simplify the limit expressions. There are questions about the implications of polynomial degrees on the limits, and some participants express uncertainty about how to begin solving the problems.

Discussion Status

The discussion is active, with some participants offering tips on how to approach the limits. One participant has successfully solved the first limit after applying the suggested method. However, there is still exploration regarding the second limit and the general behavior of limits involving polynomials.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the extent of assistance they can provide to one another. There is an acknowledgment that limits can behave differently depending on the degrees of the polynomials involved.

Petkovsky
Messages
61
Reaction score
0

Homework Statement


lim 2^n/(2^n + 2)
n[tex]\rightarrow[/tex][tex]\infty[/tex]

lim (1/2n) + 2n/(3n+1)
n[tex]\rightarrow[/tex][tex]\infty[/tex]

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:
Physics news on Phys.org
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 =]
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
17
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K