Specifying vertical asymptotes in periodic functions in set notation

  • Thread starter SubZer0
  • Start date
  • #1
19
0
Homework Statement:
What is the general format for specifying recurring vertical asymptotes in periodic functions in set notation?
Relevant Equations:
-2pi < x < 2pi
Hi all,

What is the general set notation for specifying a vertical asymptote and domain for a periodic function? For example, if I have a periodic function which has a period of pi/2, and within that period, a vertical asymptote occurs at pi/4. The domain is R, excluding that vertical asymptote. I am presuming that I can specify it something like:

{ x: x ∈ R, x ≠ n⋅(pi/2)+(pi/4) }, where n is an integer.

Does this look correct, or completely off?

Thanks!
 

Answers and Replies

  • #2
35,125
6,871
Hi all,

What is the general set notation for specifying a vertical asymptote and domain for a periodic function? For example, if I have a periodic function which has a period of pi/2, and within that period, a vertical asymptote occurs at pi/4. The domain is R, excluding that vertical asymptote. I am presuming that I can specify it something like:

{ x: x ∈ R, x ≠ n⋅(pi/2)+(pi/4) }, where n is an integer.

Does this look correct, or completely off?

Thanks!
Looks OK to me. An example of a function with this behavior is ##f(x) = \tan(2x)##
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,377
1,038
Hi all,

What is the general set notation for specifying a vertical asymptote and domain for a periodic function? For example, if I have a periodic function which has a period of pi/2, and within that period, a vertical asymptote occurs at pi/4. The domain is R, excluding that vertical asymptote. I am presuming that I can specify it something like:

{ x: x ∈ R, x ≠ n⋅(pi/2)+(pi/4) }, where n is an integer.

Does this look correct, or completely off?

Thanks!
Let's check it out.
If n=0, then you are excluding π/4 from the domain. That's good.

If n=1, then you are excluding 3π/4 from the domain. That's good.

If n = −1, then you are excluding −π/4 from the domain. That's good.

Etc.

I'm curious about the inequality, −2pi < x < 2pi , that you have in the Relevant Equations .

Also, you can find many symbols by clicking on the icon 3rd from the right in the light blue banner at the top of the "Reply/Post thread" box.

242415

Using that, your result of
{ x: x ∈ R, x ≠ n⋅(pi/2)+(pi/4) }
becomes:
{ x: x ∈ ℝ, x ≠ n⋅(π/2)+(π/4) }

Even better, use LaTeX.
 
  • #4
19
0
Thanks, Mark44 and SammyS for your responses. Have taken on board your advice for the symbols for future posts, SammyS.
 

Related Threads on Specifying vertical asymptotes in periodic functions in set notation

  • Last Post
Replies
2
Views
12K
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
9
Views
843
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
6
Views
10K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
2
Views
1K
Top