Specifying vertical asymptotes in periodic functions in set notation

[SubZer0]

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]

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 $f(x) = \tan(2x)$

 

[SammyS]

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.

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.

 

[SubZer0]

Thanks, Mark44 and SammyS for your responses. Have taken on board your advice for the symbols for future posts, SammyS.