Okay, I need to write a professional Korean wiki-style document about vertical asymptotes for calculus under the education category. Let me start by understanding the structure. The user wants a clear H1 title, an introduction, several detailed sections with H2 and H3 headings, and possibly references or related documents.

First, the title is given as "수직점근선". The introduction should explain what vertical asymptotes are in simple terms. I should mention that they occur where a function approaches infinity as x approaches a certain value. Maybe start with the definition and their significance in calculus.

Next, the detailed sections. The user specified H2 and H3. So possible sections could be Definition and Mathematical Representation, How to Find Vertical Asymptotes, Examples, Applications in Real Life, and Related Concepts. Under each H2, maybe some H3 sub-sections.

For the definition, I need to explain the concept clearly. Mention that vertical asymptotes are vertical lines x = a where the function grows without bound. Include the mathematical notation using limits, like lim(x→a) f(x) = ±∞. Also note that they often occur at points where the function is undefined, like denominators being zero in rational functions.

How to find them: steps like identifying domain restrictions, evaluating limits. Maybe break down into steps. For rational functions, set denominator to zero and solve for x. Then check if numerator is non-zero at those points. Also, check the left and right limits to confirm if they approach infinity.

Examples: Use a rational function like f(x) = 1/(x-2). Show that as x approaches 2 from the right, f(x) approaches infinity, and from the left, negative infinity. Another example could be f(x) = tan(x), which has vertical asymptotes at x = π/2 + kπ. Explain why.

Applications in real life: Maybe in physics, engineering, economics. Like in electrical circuits where resistance approaches zero leading to infinite current, or population models approaching a carrying capacity.

Related concepts: Horizontal asymptotes, removable discontinuities, infinite limits. Maybe explain the difference between vertical asymptotes and other discontinuities.

I need to ensure accuracy. For example, when talking about rational functions, the vertical asymptotes occur at zeros of the denominator after simplifying the function. So if there's a common factor in numerator and denominator, that might be a removable discontinuity instead of an asymptote.

Also, in examples, check that the limits are correctly evaluated. For tan(x), it's periodic with vertical asymptotes at odd multiples of π/2.

For the code blocks, maybe include a simple calculation in LaTeX for the examples. Like showing the limit calculations.

Make sure to use proper markdown structure. H1 for the title, H2 for main sections, H3 for sub-sections. Use bullet points where appropriate. Maybe a table comparing vertical asymptotes with horizontal ones?

Wait, the user said if there's code or technical content, use code blocks. Since there's math notation, maybe use LaTeX in code blocks. For example, the limit expression: \lim_{x \to a} f(x) = \infty.

Also, check the length requirement. Need at least 800 characters. The content should be detailed enough. Each section should have sufficient explanation without being too verbose.

Potential mistakes to avoid: Confusing vertical asymptotes with holes. Emphasize that vertical asymptotes are different from removable discontinuities. Also, ensure that the examples correctly demonstrate the concept.

Let me structure the document step by step. Start with the title, then introduction. Then sections on definition, finding them, examples, applications, related concepts, and references. Each section with H2. Under finding them, H3 for steps. Examples can have H3 for each example.

Check for clarity and readability. Use simple Korean terms where possible, but maintain technical accuracy. Define any terms that might be unfamiliar, like "극한" (limit) if necessary.

Make sure the mathematical explanations are correct. For instance, the limit approaching from the left and right both going to infinity (same sign) or opposite signs. In the example of 1/(x-2), approaching from the right goes to +infty, left goes to -infty, so the vertical asymptote at x=2 exists.

For references, maybe include standard calculus textbooks or online resources. Since this is a wiki-style document, having a "참고 자료" section at the end.

I think that's a solid outline. Now, draft each section ensuring the markdown syntax is correct. Use bold or italics if needed, but since it's Korean, maybe use asterisks for emphasis. Tables can be used to compare concepts. Lists for steps in finding asymptotes.

Double-check that all user requirements are met: structure, content quality, markdown format, length. Once the draft is done, review for any errors or improvements.