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### A way to remember the Entire Unit Circle for Trigonometry

00:07:19Patrick JonesA way to remember the Entire Unit Circle for Trigonometry. This is the way that I remember the unit circle.

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### What is a Limit? Basic Idea of Limits

00:05:07Patrick JonesWhat is a Limit? Basic Idea of Limits and what it means to calculate a limit.

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### Finding Limits From a Graph

00:09:25Patrick JonesFinding 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.

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### Calculating a Limt By Factoring and Canceling

00:03:15Patrick JonesCalculating a Limit By Factoring and Canceling - One example is shown!

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### Calculating a Limit by Expanding and Simplfiying

00:01:50Patrick JonesCalculating a Limit by Expanding and Simplfiying.

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### Calculating a Limit by Getting a Common Denominator

00:04:53Patrick JonesCalculating a Limit by Getting a Common Denominator - One example is shown!

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### Calculating a Limit Involving sin(x)/x as x approaches zero

00:06:02Patrick JonesCalculating a Limit Involving sin(x)/x as x approaches zero.

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### Limits Involving Absolute Value

00:10:11Patrick JonesLimits 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.

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### The Squeeze Theorem for Limits, Example 1

00:07:13Patrick JonesThe Squeeze Theorem for Limits - I discuss the idea of the Squeeze Theorem as well as showing two examples illustrating the Squeeze Theorem!

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### Calculus - Infinite Limits

00:12:06Patrick JonesCalculus - Infinite Limits. In this video I calculate a few limits where the solutions are either +/- infinity or the limits do not exist.

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### Limits at Infinity - Basic Idea and Shortcuts

00:08:51Patrick JonesLimits at Infinity - Basic Idea and Shortcuts for Rational Functions.

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### Shortcut to Find Horizontal Asymptotes of Rational Functions

00:04:35Patrick JonesShortcut 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!

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### Calculating a Limit at Infinity with a Radical

00:09:11Patrick JonesCalculating a Limit at Infinity with a Radical in the Expression

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### Continuity - Part 1 of 2

00:06:25Patrick JonesContinuity - 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.

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### Continuity - Part 2 of 2

00:08:24Patrick JonesContinuity - Part 2 of 2. In this video, two complete examples are shown discussing discontinuities of a function.

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### Understanding the Definition of the Derivative

00:12:09Patrick JonesUnderstanding 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!!

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### Sketching the Derivative of a Function

00:14:49Patrick JonesSketching 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).

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### Finding a Derivative Using the Definition of a Derivative

00:07:37Patrick JonesFinding a Derivative Using the Definition of a Derivative - The long way! Two complete examples are shown.

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### Basic Derivative Examples

00:09:07Patrick JonesBasic Derivative Examples - A few examples of finding derivatives for 'easy' functions.

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### The Product Rule for Derivatives

00:08:04Patrick JonesThe Product Rule for Derivatives - A few basic examples.

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### The Quotient Rule

00:07:37Patrick JonesThe Quotient Rule for finding Derivatives - A few basic examples.

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### Basic Chain Rule Problems

00:04:46Patrick JonesBasic Chain Rule Problems - A few examples are shown. I have another video explaining the chain rule and showing more examples!

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### Using the Chain Rule - Harder Example #1

00:04:41Patrick JonesAn example is shown using the chain rule multiple times!

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### Using the Chain Rule - Harder Example #2

00:06:46Patrick JonesUsing the Chain Rule - Harder Example #2. In this video I use the Chain rule along with the quotient rule and simplify!!

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### Using the Chain Rule - Harder Example #3

00:06:28Patrick JonesUsing the Chain Rule - Harder Example #3. Just another looooong problem using the chain rule!

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### Derivatives - Product + Chain Rule + Factoring

00:02:53Patrick JonesDerivatives - Product + Chain Rule + Factoring - A quick example for a friend out there in internet land!

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### Product Rule, Chain Rule and Factoring - Ex 2

00:05:32Patrick JonesProduct 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!

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### More Complicated Derivative Examples

00:09:22Patrick JonesMore Complicated Derivative Examples - A couple of 'harder' examples where I find the derivative.

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### Finding the Equation of a Tangent Line

00:09:44Patrick JonesFinding the Equation of a Tangent Line using Derivatives - 3 complete examples are shown along with the outline of the procedure.

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### Lots of Different Derivative Examples

00:35:44Patrick JonesNeed 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.

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### Implicit Differentiation - Basic Idea and Examples

00:07:06Patrick JonesImplicit 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!

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### Using Implicit Differentiation - Extra Examples

00:07:46Patrick JonesUsing Implicit Differentiation to Find a Derivative - Extra Examples!!

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### Using Implicit Differentiation - Example

00:06:29Patrick JonesUsing Implicit Differentiation to Find a Derivative!

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### Using Implicit Differentiation to find a Second Derivative

00:06:29Patrick JonesUsing Implicit Differentiation to find a Second Derivative and simplifying!

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### More Implicit Differentiation Examples- 2

00:08:59Patrick JonesMore Implicit Differentiation Examples! An example of finding a tangent line is also given.

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### More Implicit Differentiation Examples- 3

00:07:46Patrick JonesMore examples using Implicit Differentiation to find Derivatives.

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### Related Rates #1 Problem Using Implicit Differentiation

00:09:56Patrick JonesRelated Rates Problem Using Implicit Differentiation

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### Related Rates #2 Using Cones

00:02:47Patrick JonesRelated Rates using Cones. Gravel is being dumped into a pile that forms a cone; how quickly is the height changing?

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### Related Rates #3 - A point on a graph

00:03:54Patrick JonesRelated 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

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### Related Rates #4 Involving Trigonometry

00:02:21Patrick JonesRelated Rates Involving Trigonometry - A problem from UT Austin Calculus 1, HW #8.

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### Related Rates #5 Involving Baseball

00:03:29Patrick JonesRelated Rates Involving Baseball! A problem from UT Austin Calculus 1 course, HW #8.

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### Using Differentials

00:07:37Patrick JonesUsing 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.

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### Finding the Linearization at a Point / Tangent Line Approximation

00:04:11Patrick JonesFinding the Linearization of a function at a point. A homework problem from UT-Austin's Calculus 1 class, homework set #8.

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### Increasing/Decreasing , Local Maximums/Minimums

00:05:17Patrick JonesIncreasing/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.

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### The Mean Value Theorem

00:14:36Patrick JonesThe 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.

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### Finding Critical Numbers - Example 1

00:04:42Patrick JonesFinding Critical Numbers - Example 1. In this video I show how to find the critical numbers of a rational function.

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### Finding Critical Numbers - Example 2

00:07:21Patrick JonesFinding Critical Numbers - Example 2. Another example of finding critical numbers.

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### Finding Intervals of Increase/Decrease Local Max/Mins

00:10:18Patrick JonesFinding 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.

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### Finding Local Maximums/Minimums - Second Derivative Test

00:11:26Patrick JonesFinding 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!

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### Concavity, Inflection Points and Second Derivatives

00:10:22Patrick JonesConcavity and Second Derivatives - Examples of using the second derivative to determine where a function is concave up or concave down.

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### Curve Sketching Using Calculus - Part 1 of 2

00:10:01Patrick JonesCurve 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!

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### Curve Sketching Using Calculus - Part 2 of 2

00:08:05Patrick JonesCurve 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!

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### Summary of Curve Sketching - Example 2, Part 1 of 4

00:07:52Patrick JonesSummary 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.

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### Summary of Curve Sketching - Example 2 - Part 2 of 4

00:09:07Patrick JonesSummary of Curve Sketching - Example 2 - Part 2 of 4. In this video, I discuss finding horizontal and vertical asymptotes.

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### Summary of Curve Sketching - Example 2 - Part 3 of 4

00:09:53Patrick JonesSummary 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.

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### Summary of Curve Sketching - Example 2 - Part 4 of 4

00:03:42Patrick JonesSummary of Curve Sketching - Example 2 - Part 4 of 4. In this video, I finally do the sketch!!

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### Optimization Problem #1

00:07:13Patrick JonesAn Optimization is Shown using Derivatives. I have posted another examples as well!

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### Optimization Problem #3 - Making a Rain Gutter

00:10:21Patrick JonesOptimization Problem #3 - Making a Rain Gutter! This optimization problem involves some trigonometry too!

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### Newton's Method

00:07:29Patrick JonesNewton'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.

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### The Squeeze Theorem and Absolute Value Theorem, #1

00:03:04Patrick JonesThe 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.

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