Author Archives: hangtime

The Power Rule (no U-Substitution)

So there was a power rule in derivatives with the same name, but I doubt you'll get them confused because they're exact opposites. Uh-oh, that's confusing? Don't worry, this is everyone's favorite integral formula. In this video we'll integrate some easy examples, but also show how some algebra can make harder ones doable as well.

This video appears on the page: Intro to Integration & Anti-Derivatives

Log & Exponential Integrals (without U-Substitution)

There's not a lot you can do with exponentials and logs without U-substitution, but we'll give it a try! Basically just warming up your algebra skills for the craziness waiting for you later in Calculus.

This video appears on the page: Intro to Integration & Anti-Derivatives

Trig Function Integrals (without U-Substitution)

As you've noticed by now, integral formulas are just the same as the derivative formulas, except they're backwards. Nowhere is that more confusing than with trig functions, which are confusing and complicated to begin with. But don't worry, I work examples so messy that you'll be relieved when you see the relatively straightforward stuff your teacher puts on the test.

This video appears on the page: Intro to Integration & Anti-Derivatives

Integrating Roots Radicals & Fractions (no U-Sub)

In previous chapters, we took the derivatives of roots and radicals with the power rule by turning them into fractional exponents. Not surprisingly, we're going to take the same approach with integration. Because it works. If you need to do these with u-substitution, that's in a later chapter.

This video appears on the page: Intro to Integration & Anti-Derivatives

Why The Heck Do We Need +C?

"C", otherwise known as the constant of integration, can cost you a lot of points if you forget it because it's in every freaking problem. But what does it mean? Where did it come from and where is it going? And how do I solve those pesky "initial value" problems?

This video appears on the page: Intro to Integration & Anti-Derivatives

Intro to Integration & Anti-Derivatives
The Power Rule (no U-Substitution)
Why The Heck Do We Need +C?
Integrating Roots Radicals & Fractions (no U-Sub)
Trig Function Integrals (without U-Substitution)
Log & Exponential Integrals (without U-Substitution)

Basic integration (antiderivatives) of power rule polynomials, roots & radicals, trig functions, and initial value problems, all WITHOUT u-substitution.

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

Cross Product of Vectors

Not to be confused with the dot product, which has a dot, the cross product has... an x. But it looks like a cross, kinda. A x B. That looks like a cross, right? Never mind. Just don't confuse x's with dots or your trig life will be turned upside down. N.VM.11

This video appears on the page: Vectors

i, j, k Notation

This little guys with the ^ over them are a serious pain! It's like every trig teacher in the world decided that vectors weren't hard enough already, so we're going to figure out how to make them twice as difficult to use. Well, if that was their intent, they pulled it off.

This video appears on the page: Vectors

Components of Vectors

In this video we take a look at what to do when you're given a vector's magnitude and direction (an angle), and asked to find the vector's X & Y components. We also cover how to add vectors when all you've got is their magnitude and direction.

This video appears on the page: Vectors

Magnitude & Unit Vectors

The magnitude symbols look like absolute value -- |v| -- but it just means length of the vector. In this video we'll cover that, as well as how to use magnitude to calculate the Unit Vector, which is just a vector that's only one unit long.

This video appears on the page: Vectors

The Dot Product and Scalar Product

Both these terms refer to the same process. By doing a sort of FOIL on two vectors we can find out if they're perpendicular, which is awesome because... Uh, well, at least you'll be able to answer the question on the test.

This video appears on the page: Vectors

Adding, Subtracting & Multiplying Vectors

From now on we'll mostly be dealing with vectors mathematically, using the (x,y) or (x,y,z) ordered pair form to add and subtract.

This video appears on the page: Vectors

Dealing With Vectors Graphically

This video introduces vectors, what they are and how to graph them. Then we go through every operation you can do on vectors, except that we'll do them all by graphing: addition, subtraction, multiplication by scalar, translation.

This video appears on the page: Vectors

Vectors
Dealing With Vectors Graphically
Adding, Subtracting & Multiplying Vectors
The Dot Product and Scalar Product
Magnitude & Unit Vectors
Components of Vectors
i, j, k Notation
Cross Product of Vectors

Basics of vector addition, subtraction, multiplication, dot product, scalar product, magnitude, unit vectors, cross multiplication, and components.

Part of the course(s): ,Trigonometry ,Test Image Problem ,College Algebra ,Pre-Calculus ,Calculus ,Physics

Derivatives with Variables In Both Exponent & Base

This video covers an unusual type of derivative (possibly called "logarithmic differentiation") where X is raised to the power of itself, so the power rule doesn't apply: xx and (sinX)x. If your teacher covers this, you'll need to memorize the steps I present here, because you'll never figure out the trick on these otherwise!

This video appears on the page: Super-Hard Derivatives

Unique Derivatives
Logarithmic Differntiation aka Derivatives with Variables In Both Exponent & Base

The videos in this chapter cover specific and unusual types of derivatives that I wasn't sure where else to put, such as: xx and (sinX)x.

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

L'Hopital's With Indeterminate Exponents

This is a very rare, and very difficult, type of limit problem that almost no calculus teachers make you do. But if you've got a tough teacher, this could be for you. In this video we take the limit of xx and (sinX)x, which might not look that bad, but you can't take the derivative of them any other way.

This video appears on the page: L’Hopital’s Rule

L'Hopital's With Indeterminate Fractions

This is the most common type of L'Hopital's Rule problem, taking limits of indeterminate fractions. You need derivatives for this, but once you see it, you'll be kicking yourself that your teacher made you do limits the hard way for so long!

This video appears on the page: L’Hopital’s Rule

L'Hopital's Rule
L'Hopital's With Indeterminate Fractions
L'Hopital's With Indeterminate Exponents

This shortcut for finding limits is easier than everything that's come before, but it requires taking derivatives.

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

Curve Sketching Examples

In this video I work a couple of full examples of curve sketching -- one polynomial, one rational function. These problems are monsters, including maxima and minima, asymptotes, inflection points, and of course a graph!

This video appears on the page: Inflection Points & Curve Sketching