# Specifying vertical asymptotes in periodic functions in set notation

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!

Mark44
Mentor
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)##

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SammyS
Staff Emeritus
Homework Helper
Gold Member
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 .

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