Limits explanations, examples, practice problems. Ready? Let's do this.
Limits and Graphs
Math teachers and professors across the globe try to make limits into this big, huge deal. We're here to set the record straight. In fact, that's our mission: to prove that limits are one of the mo...
Direct Substitution
Things are going great so far. These limit things are easy, right? Well, we hope so. They not too complicated so far. In fact, they won't get a whole heck of a lot tougher this section either, as w...
One-Sided Limits
One-sided limits are crucial. They are to limits in general as LeBron James is to, well, every team he plays for. Without one-sided limits, limits themselves couldn't exist. This ends up being a bi...
Properties of Limits
Time to crank this these limits up a notch or two. Or five. Five notches of cranked-upedness, one for each of the five properties of limits. Let's roll.
Advanced Limit Evaluation
We're starting to get pretty good at evaluating limits. Too bad that things are going to get a little harder from here on. Not quite "evade the man-eating llama" levels of difficult, but still.See,...
Limits at Infinity
What's the biggest thing you've ever seen? The world's largest rubber band ball? Maybe the ocean? Actually, the sun is pretty huge (understatement), and we see that every day. But then we could say...
Continuity
They're smooth as a baby's bottom, and not nearly as prone to smelly accidents. That's why we prefer continuous functions. We've thrown that term around a few times already, without really discussi...
In the Real World
Welcome, Shmooperinos, to the final section in the final chapter of Precalculus. Insert round of applause here. This last one is all about where we can find and use limits outside of our pesky math...