Prologue:On understanding the use of binomial theorem to find asymptotes of a real valued function

So i understood how to obtain non linear asymototes of a function if any. So how do you know if the function has more than one non linear asymptote? I mean look at the part of the graph "in the 3rd quadrant". How do i know it wont have any non linear asymptote "there"?

Here is the reference Question used on all my posts:

y =$$(x^3+2x+9)$$/$$(sqrt(4x^2+3x+2))$$

My asymptote obtained using long division

y=(x^2/2) -(3x/16) +(9/128)

Graph: Graph of the function and obrained asymptote

Red line: Original Function

Black line: Asymptote

  • $\begingroup$ I am planning to learn mathsjax next. $\endgroup$ – user33699 Jul 27 '17 at 8:31
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    $\begingroup$ Most of mathjax $\equiv$ putting $ around mathematical objects $\endgroup$ – Shuri2060 Jul 27 '17 at 8:32
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    $\begingroup$ Not sure on how to answer. There are an infinite number of possible non-linear asymptotes in the example you've given (and the same for a lot of other examples too). $\endgroup$ – Shuri2060 Jul 27 '17 at 8:36
  • $\begingroup$ How do you find an asymptote for the graph of the function in the "negetive part". $\endgroup$ – user33699 Jul 27 '17 at 8:38
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    $\begingroup$ I'm not sure how you got it for the positive part, but surely using the same method while applying the idea $x\to-\infty$ instead of $x\to\infty$ will work? $\endgroup$ – Shuri2060 Jul 27 '17 at 8:40

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