Can't Seem to Solve Alpha: Find the Limit

  • Context: Undergrad 
  • Thread starter Thread starter SherlockOhms
  • Start date Start date
  • Tags Tags
    Alpha Limit
Click For Summary
SUMMARY

The discussion centers on solving the limit of a function involving alpha, specifically addressing the computation of limits in complex functions. The key takeaway is that to find the limit, one should divide both the numerator and denominator by n, leading to a numerator limit of 1 and a denominator limit of 2i, as the term \(\frac{(-1)^n}{n}\) approaches 0. This approach clarifies the misconception about needing to separate the function into real and imaginary parts.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with complex numbers and their properties
  • Knowledge of the behavior of sequences, particularly \(\frac{(-1)^n}{n}\)
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the concept of limits in complex analysis
  • Learn about the behavior of sequences and series in calculus
  • Explore techniques for manipulating complex functions
  • Review examples of limits involving oscillating sequences
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus and complex analysis, as well as anyone looking to deepen their understanding of limits in mathematical functions.

SherlockOhms
Messages
309
Reaction score
0
ImageUploadedByPhysics Forums1363212190.536477.jpg


See attached image.
Can't seem to get alpha to compute this. Had this in a test and it stumped me. Could someone explain how to find the limit? Thanks in advance guys.
 
Physics news on Phys.org
Just divide top and bottom by [itex]n[/itex]. Then the limit of the numerator is 1, while the limit of the denominator is [itex]2i[/itex] (the [itex]\frac{(-1)^n}{n}[/itex] has magnitude which tends to [itex]0[/itex]).
 
Cool, thanks man. I was under impression that I had to separate the function up into it's real and imaginary parts.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 53 ·
2
Replies
53
Views
7K