Hood math explains calculus limit.from @arrionknight

Transcript

I went bad for band with Mamman. Now Jay Marsh called me out and said he was gonna go band for band. So I told him, let's set up the limit. Let's go band for band. This means we're gonna compare the order growth of my bread and Jay Marsh's bread. So we see my bread grows at 10 n parentheses n plus one, while Jay Marsh's bread grows at n squared. So we're gonna set up a limit with my bread on top and his bread on the bottom. Now here's our limit. In our numerator, we have parenthesis, so you know we gotta get rid of that. So our new numerator is gonna be 10 n squared plus 10 no, but we can simplify this limit more though. We're gonna split it into two separate fractions. It's the same thing as above. It just looks a little different. Let's make the first fraction look better. So we have 10 n squared over n squared. And n squared over n squared, we know that's one. So boom, we get rid of that. And 10 times one is 10, so we got 10 now. And for the other fraction, we have 10 n over n squared rank this simplifies down to 10 over n. And we end up with the limit as n approaches infinity of the expression 10 plus 10 over no, and 10 over n becomes zero. And this happens because as n gets bigger, the number shrinks. For example, let's say n is equal to one. Then we have 10 over one and that's equal to 10. Right? Now let's say we have n is equal to a 100. Now we're gonna get 0.1. You see, it gets smaller and smaller and smaller as we go higher. So that's why we just represent it as a tier. And we're left with the answer just being 10. 10 is a constant, and if we get a constant, that means that we have the same order of growth. So as n approaches infinity, this means that me and j Mars have the same amount of motion. And we can write this as 10 n times n plus one is theta of n squared.