Okay, I need to write professional and useful wiki document about "점근선" (asymptotes) the given categories: Education Mathematics, Calculus. Let me start by recalling what asymptotes are. They are lines that a graph approaches but never touches. There are three types: horizontal, vertical, and obliqueFirst, the structure. user specified a clear (H1), then an overview/introduction section. After that, several sections with details using H2 and H3. Maybe include sections for each type of asymptote. Also, mention the importance in calculus, like limits and behavior of functions.

For the introduction, I should explain what asymptotes are in simple terms, maybe their significance in graphing functions. Then, under each type, I'll define them, give examples, and perhaps mathematical criteria. For vertical asymptotes, functions like rational functions where the denominator approaches zero. Horizontal asymptotes relate to limits as x approaches infinity. Oblique asymptotes occur when the degree of the numerator is one more than the denominator, requiring polynomial division.

I need to ensure accuracy. Let me verify the conditions for each asymptote. Vertical asymptotes occur where the denominator is zero and the numerator isn't. Horizontal asymptotes depend on the degrees of numerator and denominator polynomials. For oblique, yes, the degree difference is one, and the quotient from division gives the line.

Examples will help. For vertical, maybe f(x) = 1/(x-2). Horizontal could be f(x) = (2x² + 3)/(x² - 1), approaching y=2. Oblique: f(x) = (x³ + 2x)/(x² + 1), divide to get y=x.

Also, mention how asymptotes relate to limits. Vertical asymptotes involve limits approaching infinity as x approaches a point. Horizontal asymptotes are limits at infinity. Oblique is similar but with a linear function.

In the applications section, explain how they help in graph sketching, understanding function behavior, and real-world uses like in economics for trends or physics for limits.

Need to include technical terms but explain them. For instance, define limits, rational functions, degrees of polynomials. Use markdown for equations, maybe LaTeX syntax.

Check for markdown structure: H1 title, H2 sections, H3 subsections. Use bullet points for types, tables if needed for comparisons. Code blocks for equations, like:

$$ f(x) = \frac{1}{x} $$ $$ y = \lim_{x \to \infty} f(x) $$

Length should be at least 800 characters. Let me estimate. Introduction (100), each type 200 each (3 types = 600), applications 100, related topics 100. That's around 900, which should be enough.

Need to avoid any markdown errors. Ensure proper headers, no missing sections. Also, references or related materials at the end. Maybe suggest calculus textbooks or related topics like limits, continuity.

Wait, the user mentioned "참고 자료나 관련 문서 섹션" which is references or related documents. So include that. Also, use bold for key terms when first introduced.

Let me outline the sections:

1. 제목: 점근선 (H1)
2. 개요 (Introduction)
3. 수직 점근선 (Vertical Asymptote)
4. 정의
5. 수학적 조건
6. 예시
7. 수평 점근선 (Horizontal Asymptote)
8. 정의
9. 수학적 조건
10. 예시
11. 기울기 점근선 (Oblique Asymptote)
12. 정의
13. 수학적 조건
14. 예시
15. 중요성 및 응용 (Importance and Applications)
16. 관련 문서 (Related Documents)

Make sure each section flows logically. Use examples to clarify. Check that all terms are explained. Avoid overly complex language but maintain professionalism. Use tables to compare asymptotes, maybe their conditions and examples.

For example, a table comparing vertical, horizontal, oblique:

That could be helpful. Also, use code blocks for equations. Ensure that all mathematical expressions are properly formatted.

I should also mention cases where there's no asymptote, like if numerator and denominator both approach zero, leading to holes instead of asymptotes. But maybe that's more in rational functions, so include a brief note.

Double-check the mathematical conditions. For vertical asymptotes, the limit must be infinite as x approaches a certain point. For horizontal, limit as x approaches ±∞. For oblique, the difference between function and line approaches zero as x approaches ±∞.

Also, note that some functions can have multiple vertical asymptotes. For example, tan(x) has infinitely many vertical asymptotes at π/2 + kπ.

In applications, maybe mention how asymptotes are used in engineering for system stability analysis, or in biology for population models approaching carrying capacity.

Make sure the document is in Korean, using the correct terminology. Terms like "수직 점근선", "수평 점근선", "기울기 점근선" are correct. Also, "유리 함수" for rational functions.

Now, start drafting each section, keeping paragraphs concise and using subsections where appropriate. Use bold for key terms when first introduced. Ensure examples are clear and equations are properly formatted.