Author Archives: hangtime

Limits At Infinity

This video covers what to do if X is approaching infinity (or negative infinity) in lots of different situations: polynomial fractions, complex fractions, polynomials. I'll also show you a great trick that will cut your factoring time by 90% for these problems!

This video appears on the page: Limits at Infinity & Asymptotes

Limits at Infinity & Asymptotes
Limits At Infinity
Using Limits To Find Horizontal Asymptotes

This chapter covers what to do when X is approaching infinity (the sideways 8 symbol), as well as how we can use this new skill to find horizontal asymptotes of rational functions.

Part of the course(s): ,Test Image Problem ,Calculus

Limits With Roots & Radicals

As always, every problem in this video will start with trying to plug in the number and seeing if we get lucky! That won't usually work, though, at which point we'll rely on the classic algebra tricks for rationalizing denominators, which work surprisingly well on limits. (If you're not a fan of working with roots, check out the roots & radicals chapter.

This video appears on the page: Limits of Giant Fractions

Limits of Polynomial Fractions

This video covers what to do if X is approaching a number, like 2 or 5. For polynomial problems where X is approaching infinity, check out the Limits At Infinity chapter. Also, there is a lot of factoring in this video, so if you're not a fan of factoring, check out my factoring chapter.

This video appears on the page: Limits of Giant Fractions

Limits of Giant Fractions (Rational Functions)
Limits of Polynomial Fractions: Plugging in
Limits of Polynomial Fractions: Indeterminate, Infinite, and "Does Not Exist" solutions
Limits of Polynomial Fractions: Difference of Cubes
Limits of Polynomial Fractions: U-Substitution
Limits With Roots & Radicals

These are your classic "big mess of algebra" limit problems, which happen when a limit is "indeteriminate" (plugging in results in 0/0 or infinity/infinity). This chapter covers finding limits of "giant fractions" (i.e. rational expressions) containing polynomials and roots & radicals.

Part of the course(s): ,Test Image Problem ,Calculus

One-Sided Limits Analytically (Algebraically)

In the first video we covered one-side limits based on graphs. In this video we cover left-hand and right-hand limits in equation form, including how to tell if they're approaching positive or negative infinity. Plugging in, as usual, is our best strategy!

This video appears on the page: One-Sided Limits

One-Sided Limits
One-Sided Limits
One-Sided Limits Analytically (Algebraically)

One-sided limits are the ones where you're approaching x from either the right or the left. 3+ means limit approaching 3 from the right, 3- means approaching 3 from the left.

Part of the course(s): ,Test Image Problem ,Calculus

Continuity
Does Limit Exist?
Continuity (i.e. is a function continuous)

This chapter covers how to figure out if a function is continuous from both a graphical and limit perspective, including the definition of continuous.

Part of the course(s): ,Test Image Problem ,Calculus

Limits of Piecewise Functions

You probably thought (and hoped) that you'd left piecewise functions behind back in Pre-Calc, but no, here we go again. Your class or teacher might not cover these, but if you have a harder teacher you probably will. They're very similar to the graphical problems from earlier videos in this chapter, except with these they won't give you the crazy graph to analyze: you'll have to graph it yourself.

This video appears on the page: Intro to Limits

Continuity (i.e. is a function continuous)

This is one of those lawyer-type questions you get into in calculus from time to time. There is a very specific definition of continuity that you have to know for your test and the AP test, and you have to know how to apply it in order to figure out if a function is continuous or not. Annoying, I know, but hey, we'll be getting confused by differentiation rules instead soon enough!

This video appears on the page: Continuity

Does Limit Exist?

This video is very short and covers material I've mentioned in other limit videos as well, but I made this a separate video because it's the #1 most confusing topic in limits, based on my experience tutoring calculus students over the years. Whether you're in AP, college, or regular, you don't want to miss this one.

This video appears on the page: Continuity ,Intro to Limits

One-Sided Limits

Also called "right-handed" and "left-handed" limits, these are the ones where they put a little plus or minus sign to the right of the number. For example, 2+ would mean "limit as x approaches 2 from the right." These have a lot of graphing to them, so you'll definitely want to watch the previous video about graphical limits first.

This video appears on the page: One-Sided Limits

Graphically Determining Limits

These are the problems where they give you a crazy graph with lots of holes and asymptotes and weird jumps and ask you what the limit is at a few random values of x. Not sure what I'm talking about? You will when you see them. Key concepts here for the rest of the limits chapter.

This video appears on the page: Intro to Limits

What The Heck Are Limits? (free)

We're about to find out. Big time! In this video I explain what they are, and show you the first step you'll try in almost every limit problem you ever see. I also give an overview of the types of problems we'll see in later videos, to sort of give you a heads up. Don't miss this video!

This video appears on the page: Intro to Limits ,free videos edit ,Free Sample Videos ,calculus free videos

Intro to Limits:
Graphical limits
Piecewise Functions
Does the limit exist?

The videos in this chapter cover the more conceptual side of limits. In the first video we cover what limits are, and give an overview of the various types of limit problems you'll see in calculus. The rest of the videos cover analyzing graphs for limits, figuring out if the limit "exists", and finding the limits of piecewise functions.

Part of the course(s): ,Test Image Problem ,Calculus

Midpoint Formula

Back to no proofs on this one! We'll just learn this simple formula, and use it on a couple of basic problems before embarking on an awesome word problem example where we'll find the midpoint between L.A. and New York, and even find the name of the Kansas town nearest to it!

This video appears on the page: Distance & Midpoint Formulas ,Midpoint Definition & Formula

The Distance Formula

Normally I pride myself on not deriving anything, since 99% of the time that infuriates students. However, in the case of the distance formula, I've found over my years of tutoring that showing how it came from the Pythagorean Formula is actually really helpful for students trying to memorize and use the formula. So I do that here. But if you hate it, you can always skip the first half of the video! Don't miss the word problem though.

This video appears on the page: Distance & Midpoint Formulas

Distance & Midpoint Formulas
Distance Formula: Derivation
Distance Formula: Word Problem
Midpoint Formula

This chapter teaches you the formulas for finding the distance and midpoint between two points on the X-Y plane, as well as word problems using these formulas.

Part of the course(s): Middle School Math ,Geometry ,Pre-Algebra Class Page ,College Algebra ,Algebra

The Pythagorean Theorem

It seems like they're teaching kids this theorem younger and younger, sometimes before students even learn how to solve an equation. So in this video I take this thing from the very basics. Word to the wise: Pythagorean Theorem only works on right triangles!

This video appears on the page: Pythagorean Theorem

The Pythagorean Theorem

It seems like they're teaching kids this theorem younger and younger, sometimes before students even learn how to solve an equation. So in this video I take this thing from the very basics. Word to the wise: Pythagorean Theorem only works on right triangles!