**Math 3A**

Differential and Integral Calculus I

- Khan Academy: Limit at a point of discontinuity
Video - 6:20 One-sided limit example - Khan Academy: Limit Example 1
Video - 5:44 Limits by cancelling factors - Khan Academy: Limits and infinity
Video - 7:41 Intro to limits involving infinity - Khan Academy: More limits at infinity
Video - 4:33 Limits to infinity (non-rigorous) This video uses a handy short-cut to solve limits. The more general method (which your prof may require) is given in the previous video - Calculus Applets: Formal Definition of Limits
Interactive Formal (delta-epsilon) definition of a limit - PatrickJMT: Calculating a Limit by Multiplying by a Conjugate
Video - 4:09 Limits of rational functions with square roots - PatrickJMT: Calculating a Limit at Infinity With a Radical
Video - 9:11 Limits of rational functions with square roots to infinity - PatrickJMT: Limits at Infinity - Basic Idea and Shortcuts!
Video - 8:51 Finding limit of a linear-to-linear function at infinity (analytic method) - Paul's Notes: Limits Chapter
Text Textbook-style explanation of limits "Computing Limits" page has lots of examples

- Calculus Applets: Derivative at a Point
Interactive Visualizing derivative as a limit - Khan Academy: Derivative Intuition
Interactive Visualizing derivative functions - Mathispower4u: Determining Derivatives Using The Limit Definition
Video - 10:27 Three examples on finding derivatives using the limit definition

- Derivative Cheatsheet/Worksheet
Text All 3A derivative rules with examples and exercises - Khan Academy: Applying the Product Rule for Derivatives
Video - 2:40 Product rule explained well See exercises as well - Khan Academy: Quotient Rule for Derivative of tan(x)
Video - 3:42 Quotient rule explained well See exercises as well - Khan Academy: Chain Rule Definition and Example
Video - 5:31 Chain rule explained well See next few videos for more examples. See exercises as well. - Khan Academy: Chain Rule for Derivative of 2^x
Video - 4:48 Change-of-base for exponents See next video for change-of-base for logarithms. - Khan Academy: Implicit Differentiation
Video - 8:02 Implicit differentiation explained well See next few videos for more good examples. - Khan Academy: Derivative of x^(x^x)
Video - 9:02 Logarithmic differentiation example - PatrickJMT: Logarithmic Differentiation - Example 3
Video - 3:40 Logarithmic differentiation example

- Khan Academy: Introduction to l'Hopital's Rule
Video - 8:51 l'Hospital's rule See next few videos for more examples. See exercises as well. - Paul's Notes: l'Hospital's Rule
Text l'Hospital's rule examples Includes some harder ones - Khan Academy: Rates of Change Between Area and Radius of a Circle
Video - 7:43 Related rates example See next few videos for more examples. - Khan Academy: AP Calculus Practice Questions
Video Database Lots of word problems with derivatives

- Khan Academy: Minima, maxima and critical points
Video - 7:52 Critical points explained well - Khan Academy: Identifying minima and maxima
Video - 9:42 How to test whether a critical point is a local max, local min, or neither - Mathispower4u: Determining Relative Extrema Using The First Derivative Test
Video - 6:18 How to use first derivative to find relative extrema - Paul's Notes: Abslute Extrema
Text Finding absolute extrema on an interval (with word problems)

- Curve Sketching Worksheet
Text Guided curve-sketching examples - Khan Academy: Graphing using derivatives
Video - 20:31 Long, but very good. - Khan Academy: Another example graphing with derivatives
Video - 25:08 Long, but very good.