# On predicting whether a real valued function has a non linear asymptote or not.

Suppose I have two functions.

1. $$y= \frac{x^3+2x +9}{\sqrt{4x^2+3x+2}}$$ which has an non linear asymptote of $y=\dfrac{x^2}2-\dfrac{3x}{16}+\dfrac{251}{256}$.

2. $$y = \frac{x}{(x^4 + 1)^{1/4}}$$ which has a linear asymptote of $y=1$.

How can I predict which function may have a non linear asymptote?

• Forgive for the editing. – user33699 Jul 17 '17 at 10:49
• Welcome to StackExchange! I have edited your question using MathJax, check that I haven't made any errors, and also click edit to see how it works. – lioness99a Jul 17 '17 at 11:01
• i think you meant $$\frac{x^3+2x+9}{\sqrt{4x^2+3x+2}}$$ – Dr. Sonnhard Graubner Jul 17 '17 at 11:02
• @lioness99a thanx i appreciate your effort – user33699 Jul 17 '17 at 11:03
• @Dr.SonnhardGraubner yes there has been an error on this part :( – user33699 Jul 17 '17 at 11:05

HINT: $$f(x)=\frac{x}{\sqrt[4]{x^4+1}}=\frac{x}{|x|\sqrt[4]{1+\frac{1}{x^4}}}$$