Category Archives: calculus

Tweet5.2: The Definite Integral Remember last time when we talked about a special kind of limit? The limit of a sum of rectangles where you get the area under a curve by using smaller and smaller rectangles? That special limit … Continue reading →

TweetInteresting Problems in 5.1 A lot of these were a bit easy, but were designed to give you intuition. So, best to go through some of these on your own, if you found the limit-of-a-summation thing confusing. That said, much … Continue reading →

Tweet5.1: Areas and Distances HOO BOY we’re getting to some more fun stuff. Now then, let’s talk about area. Area is a function of length times width. Usually, we think of this as a rectangle. There’s a reason that, when … Continue reading →

TweetChapter 4 Review and Calc 1 Wrap-up After giving it a bit of thought, I’ve decided to not personally work the problems in this section. That you can do on your own, but if you’ve followed along so far, it … Continue reading →

Tweet4.9: Antiderivatives Wow! Well, we’re on the final chapter of Calc 1. Awesome! It’s been a fun ride going back through this and strengthening my understanding. For those of you following along, I hope it’s been entertaining. Antiderivatives are really … Continue reading →

TweetInteresting Problems in 4.8 Welllll, I’m back. Sorry for the long delay, but I’ve been all over the damn country in the last month or so, for a bunch of events. I’m finally back home and settled in enough to … Continue reading →

Tweet4.8: Newton’s Method Suppose you need to figure out the root(s) of an equation, but you know it’s going to be a real bitch to solve. Like, the example in the book is Shitballs. There’s no way you’re intuiting that … Continue reading →

TweetInteresting Problems in 4.7 WOOF, these problems took a while. I ended up working through about 20, and I’ll present you the idea behind 5. However, the important general lesson for these simple optimization problems is this: basically what you’re … Continue reading →

Tweet4.7: Optimization Problems Optimization problems are basically any math problems whose last sentence contains a superlative. “What is the smallest…” “what is the closest…” “what is the longest…” They’re optimization problems in that you’re finding values of a function that … Continue reading →

Tweet4.6: Graphing with Calculus and Calculations Honestly, I think sections like this are rarely useful. Or, more to the point, you’re probably better off playing around in Wolfram Alpha for a few hours than doing this section. Anyone who’s even … Continue reading →