We will now do another substitution technique (the other was u-substitution) where we substitute variables with trig functions. This allows us to leverage some trigonometric identities to simplify the expression into one that it is easier to take the anti-derivative of.
This 19-minute video lesson provides an Introduction to the Line Integral.
This 22-minute video lesson provides an introduction to the surface integral.
This video looks at the intuition for second Fundamental Theorem of calculus.
This video looks at intuitively drawing the antiderivative of a function.
This video covers intuitively drawing the derivative of a function.
This video considers if the power rule reasonable.
Tis 8-minute video lesson demonstrate's an example of L'Hopital's Rule.
This 5-minute video lesson provdes a second example of L'Hopital's Rule.
This 8-minute video lesson provides a third example of L'Hopital's Rule.
This video shows Limit example 1.
This 9-minute video lesson presents some limit exercises.
This 7-minute video lesson presents more limit examples.
This 10-minute video lesson presents more limit examples.
This 15-minute video lesson looks at 3 interesting limit examples.
This tutorial introduces a "formal" definition of limits. So put on your ball gown and/or tuxedo to party with Mr. Epsilon Delta (no, this is not referring to a fraternity). This tends to be covered early in a traditional calculus class (right after basic limits), but we have mixed feelings about that. It is cool and rigorous, but also very "mathy" (as most rigorous things are). Don't fret if you have trouble with it the first time. If you have a basic conceptual understanding of what limits are (from the "Limits" tutorial), you're ready to start thinking about taking derivatives.
This video shows Limit properties.
This video looks at the Limit at a point of discontinuity.
This series of videos focusing on calculus covers limit introduction, squeeze theorem, and epsilon-delta definition of limits.
Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve.