How can I find asymptote of the following function ?

$y=x^{3}y^{2} - \sin(x)$

Is there a way except finding $y$ directly ?

  • 1
    $\begingroup$ Intuitively, if $x$ is very large, $y$ has to be very small to make $y-y^2x^3=\sin x$. $\endgroup$ – Arthur Dec 4 '16 at 9:41
  • $\begingroup$ Ever heard of quadratic equations? $\endgroup$ – Ivan Neretin Dec 4 '16 at 10:31
  • $\begingroup$ Here's a plot for $(x,y) \in (-20,20) \times (-1,1)$: i.stack.imgur.com/wrMLW.png $\endgroup$ – Antonio Vargas Dec 4 '16 at 11:53
  • $\begingroup$ @ Ivan Neretin: ys i know.. i can calculate y in terms of x but i want to know if i can find the asymptote without finding y. $\endgroup$ – Suman Samadder Dec 4 '16 at 17:21

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