[tex]\bf \lim\limits_{x\to \infty}~-4x^9-3x^3+2x-11 \\\\\\ \lim\limits_{x\to \infty}~-4x^9~~+~~\lim\limits_{x\to \infty}~-3x^3~~+~~\lim\limits_{x\to \infty}~2x~~+~~\lim\limits_{x\to \infty}~-11[/tex]
for any positive value of "x" as it races off towards ∞, our first limit of -4x⁹ will give us a rather large negative value, our second limit of -3x³ will also give us a large negative value and both will combine to produce an even larger negative value.
our third limit of 2x will give us a positive value, however a much smaller than its previous siblings, and our last limit is just a fixed of -11, not moving at all.
since the negative values are moving faster than the positive ones, and thus overwhelming the positive ones, the limit will increasingly be racing towards -∞.
