Concavity and Second Derivatives - Examples of using the second derivative to determine where a function is concave up or concave down.
A way to remember the Entire Unit Circle for Trigonometry. This is the way that I remember the unit circle.
What is a Limit? Basic Idea of Limits and what it means to calculate a limit.
Finding Limits From a Graph. In this video, I discuss basic limit notation and how to find many limits from a given graph. Just a basic intuitive idea of what is going on.
Calculating a Limit By Factoring and Canceling - One example is shown!
Calculating a Limit by Expanding and Simplfiying.
Calculating a Limit by Getting a Common Denominator - One example is shown!
Calculating a Limit Involving sin(x)/x as x approaches zero.
Limits Involving Absolute Value - In this video I do two limit problems that involve | absolute value | . I discuss the basic algebraic idea of how to get started on these problems.
The Squeeze Theorem for Limits - I discuss the idea of the Squeeze Theorem as well as showing two examples illustrating the Squeeze Theorem!
Calculus - Infinite Limits. In this video I calculate a few limits where the solutions are either +/- infinity or the limits do not exist.
Limits at Infinity - Basic Idea and Shortcuts for Rational Functions.
Shortcut to Find Horizontal Asymptotes of Rational Functions. In this video, I point out a couple of tricks that make finding horizontal asymptotes of rational functions very easy to do!
Calculating a Limit at Infinity with a Radical in the Expression
Continuity - The basic idea of what it means for a function to be continuous at a x = a is discussed! This is only a general intuitive idea! Concrete examples are worked out in another video.
Continuity - Part 2 of 2. In this video, two complete examples are shown discussing discontinuities of a function.
Understanding the Definition of the Derivative - In this video, I produce the definition of the derivative by thinking about slopes of tangent lines! I DO NOT use the definition of the derivative to actually calculate the derivative, although I have videos on that too!!
Sketching the Derivative of a Function - In this video, I sketch the derivative of two different functions. That is, I give the graph of y = f(x), and do a rough sketch of the graph f ' (x).
Finding a Derivative Using the Definition of a Derivative - The long way! Two complete examples are shown.
Basic Derivative Examples - A few examples of finding derivatives for 'easy' functions.
The Product Rule for Derivatives - A few basic examples.
The Quotient Rule for finding Derivatives - A few basic examples.
Basic Chain Rule Problems - A few examples are shown. I have another video explaining the chain rule and showing more examples!
An example is shown using the chain rule multiple times!
Using the Chain Rule - Harder Example #2. In this video I use the Chain rule along with the quotient rule and simplify!!
Using the Chain Rule - Harder Example #3. Just another looooong problem using the chain rule!
Derivatives - Product + Chain Rule + Factoring - A quick example for a friend out there in internet land!
Product Rule, Chain Rule and Factoring- Ex 2. In this video, I use the product rule and the chain rule to find a derivative and then use some algebra to clean it up!
More Complicated Derivative Examples - A couple of 'harder' examples where I find the derivative.
Finding the Equation of a Tangent Line using Derivatives - 3 complete examples are shown along with the outline of the procedure.
Need to see a bunch of random derivative problems? Has it been a while since you took Calculus 1 and you have forgotten some of your formulas? In this video I do 25 different derivative problems using derivatives of power functions, polynomials, trigonometric functions, exponential functions and logarithmic functions using the product rule, chain rule, and quotient rule.
Implicit Differentiation - Basic Idea and Examples. In this video, I discuss the basic idea about using implicit differentiation. That is, I discuss notation and mechanics and a little bit of the idea. I also work out a couple of examples!
Using Implicit Differentiation to Find a Derivative - Extra Examples!!
Using Implicit Differentiation to Find a Derivative!
Using Implicit Differentiation to find a Second Derivative and simplifying!
More Implicit Differentiation Examples! An example of finding a tangent line is also given.
More examples using Implicit Differentiation to find Derivatives.
Related Rates Problem Using Implicit Differentiation
Related Rates using Cones. Gravel is being dumped into a pile that forms a cone; how quickly is the height changing?
Related Rates - A point is moving on a graph, and we want to find out the rate at which the x-coordinate is changing. A problem from UT Austin Calculus 1 course, HW #8
Related Rates Involving Trigonometry - A problem from UT Austin Calculus 1, HW #8.
Related Rates Involving Baseball! A problem from UT Austin Calculus 1 course, HW #8.
Using Differentials to approximate the value (18)^(1/4). In this video, I show the basic idea of differentials and show how they can be used to approximate values.
Finding the Linearization of a function at a point. A homework problem from UT-Austin's Calculus 1 class, homework set #8.
Increasing/Decreasing , Local Maximums/Minimums - The basic idea! In this video, I just give a graph and discuss intervals where the function is increasing and decreasing. I also discuss local maximums and minimums.
The Mean Value Theorem - In this video, I explain the MVT and then I find values of c in a certain interval for a particular function.
Finding Critical Numbers - Example 1. In this video I show how to find the critical numbers of a rational function.
Finding Critical Numbers - Example 2. Another example of finding critical numbers.
Finding Intervals of Increase/Decrease Local Max/Mins - I give the basic idea of finding intervals of increase/decrease as well as finding local maximums and minimums.
Finding Local Maximums/Minimums - Second Derivative Test. In this video, I discuss how to use the second derivative test to find local maximums and local minimums. The basic idea and a few examples are shown!
Concavity and Second Derivatives - Examples of using the second derivative to determine where a function is concave up or concave down.
Curve Sketching Using Calculus - Part 1of 2. In this video I discuss the following topics to help produce the graph of a function: domain, x-y intercepts, symmetry of the function, intervals of increase/decrease, local maximums and minimums, concavity, inflection points, horizontal and vertical asymptotes (whew!). all of this is too much for one 10 minute video, so the rest is in part 2!
Curve Sketching Using Calculus - Part 2 of 2. In this video I discuss the following topics to help produce the graph of a function: domain, x-y intercepts, symmetry of the function, intervals of increase/decrease, local maximums and minimums, concavity, inflection points, horizontal and vertical asymptotes (whew!). all of this is too much for one 10 minute video, so the rest is in part 2!
Summary of Curve Sketching - Example 2, Part 1 of 4. This is a video using calculus and algebra to sketch a curve. In this video, I discuss domain, intercepts and symmetry.
Summary of Curve Sketching - Example 2 - Part 2 of 4. In this video, I discuss finding horizontal and vertical asymptotes.
Summary of Curve Sketching - Example 2 - Part 3 of 4. In this video, I discuss the first and second derivative, as well as intervals of increase/decrease, concavity, local maximums and minimums, and points of inflection.
Summary of Curve Sketching - Example 2 - Part 4 of 4. In this video, I finally do the sketch!!
An Optimization is Shown using Derivatives. I have posted another examples as well!
Optimization Problem #3 - Making a Rain Gutter! This optimization problem involves some trigonometry too!
Newton's Method - I discuss the basic idea of Newton's Method and how to use it. I do one example using Newton's Method to approximate a root.
The Squeeze Theorem and Absolute Value Theorem, #1. Here we look at finding the limits of some sequences by using the squeeze and / or absolute value theorems.