Here's information on how to find horizontal asymptotes:
To find <a href="https://www.wikiwhat.page/kavramlar/horizontal%20asymptotes">horizontal asymptotes</a> of a function, you primarily examine the function's behavior as x approaches positive and negative infinity. There are three general scenarios to consider:
Degree of Numerator < Degree of Denominator: If the degree (highest power of x) in the numerator is less than the degree in the denominator, the horizontal asymptote is y = 0. This occurs because as x becomes very large (positive or negative), the denominator grows much faster than the numerator, causing the fraction to approach zero.
Degree of Numerator = Degree of Denominator: If the degrees of the numerator and denominator are equal, the horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator). This means you divide the numbers in front of the highest power of x from the numerator and denominator. This is because, as x approaches infinity, the terms with the highest power of x will dominate the behavior of the function.
Degree of Numerator > Degree of Denominator: If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there may be a slant (oblique) asymptote. In such cases, the function tends toward infinity (positive or negative) as x approaches infinity.
Formal Method (Limits):
The most rigorous method involves evaluating the following limits:
If either of these limits exists and equals a finite number L, then y = L is a horizontal asymptote. It's possible to have different horizontal asymptotes as x approaches positive and negative infinity.
Important Considerations:
Ne Demek sitesindeki bilgiler kullanıcılar vasıtasıyla veya otomatik oluşturulmuştur. Buradaki bilgilerin doğru olduğu garanti edilmez. Düzeltilmesi gereken bilgi olduğunu düşünüyorsanız bizimle iletişime geçiniz. Her türlü görüş, destek ve önerileriniz için iletisim@nedemek.page