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Playing with some numerical simulations, I plotted this in Wolfram Cloud / Mathematica:
##x^3-\frac{x^5}{x^2+2}##
I had naively expected it to approach ##x^3−x^3=0##, but that isn't the case. It approaches 2x.
I can now vaguely understand that the two terms need not cancel at infinity, but I'd like to get a better handle on this.
[1] How to break this down intuitively and estimate the qualitative nature of the asymptote "by inspection"?
[2] How can we obtain the asymptote ##2x## theoretically?
[3] Can we find the equation of the asymptote using Mathematica etc?
[Moderator's note: Moved from a technical forum and thus no template.]
##x^3-\frac{x^5}{x^2+2}##
I had naively expected it to approach ##x^3−x^3=0##, but that isn't the case. It approaches 2x.
I can now vaguely understand that the two terms need not cancel at infinity, but I'd like to get a better handle on this.
[1] How to break this down intuitively and estimate the qualitative nature of the asymptote "by inspection"?
[2] How can we obtain the asymptote ##2x## theoretically?
[3] Can we find the equation of the asymptote using Mathematica etc?
[Moderator's note: Moved from a technical forum and thus no template.]
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