Limits with infinity
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When working with infinity in a limit, first assess if the highest power of x occurs in the numerator or denominator. That side of the fraction will grow to infinity the quickest.
When you divide anything by infinity... it'll equal zero!
When the highest power of x occurs in the denominator, it is bottom-heavy and shrinks quickly. Therefore, the limit goes to 0.
Infinity over anything... will equal infinity!
When the highest power of x occurs in the numerator, it is top-heavy and grows quickly. Therefore, the limit goes to infinity.
The highest power in both the numerator and denominator is 2... so these terms (when we plug in infinity) will overpower any smaller powers (which is why we crossed the smaller terms out).
PRO TIP: ∞2 is so much larger than ∞, that it pretty much makes ∞ obsolete. Likewise, ∞3 is so much larger than ∞2, that it makes ∞2 obsolete. And so on. This is why when working with limits going to infinity, we only need to focus on the highest power of x!
When the numerator and denominator both have the same highest power of x, the limit is the ratio of the coefficients of the highest power of x!