Calculus 1

In this video, I introduce how to find the slope of the tangent line based on the slopes of similar secant lines.

In this video, we go over the basic definition of a limit. And discuss right-sided limits versus left-sided limits, and when a limit does not exist.

In this video, we will walk through how to evaluate linear, polynomial, and rational limits by plugging in “a”.

In this video, I quickly go over some useful limit laws and also discuss the squeeze theorem.

What happens when your function approached infinity or negative infinity? What exactly is a horizontal asymptote? Find out the answers in this video!

What happens to our function as x approaches infinity or negative infinity? What is a horizontal asymptote? Find out in this video!

In this video, I introduce slant/ oblique asymptotes and give a review on vertical and horizontal. This is great limit practice, and is helpful for understanding and visualizing functions!

In this video, I address what makes a function continuous and the three items to check. I also talk about points of discontinuity and why they exist.

So far, we’ve used words such as “approaching” or “getting closer to”, but now we are going to formally or precisely define what that means by using epsilon and delta. Let’s revisit these limits!

What is the derivative? What does it have to do with slope? Why does it matter? Find out about the derivative in this introduction example video!

What is the derivative of a function? From the last video, we know how to find the derivative at any point, but taking the limit over and over again will be tedious. Let’s learn how to find a function for the derivative!

Now that we understand how to find the derivative of a function, let’s learn some ways to make it easier! In this video, we will go over the constant rule, power rule, constant multiple rule, and sum rule. All techniques that make taking the derivative a quick task!

We will continue in this video with learning rules for differentiation. We will complete examples of the product rule and quotient rule as well as products with products and quotients. Try to come up with some examples on your own to give a friend or peer!

In this video, we will go over the 6 basic derivatives of trig functions. It may seem like a lot to memorize, but there’s a pattern that will make it easier!

In this video, I introduce rates of change, but we’ve actually be doing them for some time now! Take a look at how position, speed, and acceleration are all related.

Our next technique for differentiation is the Chain Rule. This will help us take derivatives of functions within functions!

What if we can’t isolate “y”? Can we still take the derivative? Yes! With Implicit Differentiation we can easily take the derivative. Just don’t forget the Chain Rule!

In this video, we will discuss the derivative of the natural log as well as using that knowledge to accomplish the derivative of exponential functions and logarithmic differentiation.

In this video, we will learn how to find the derivative of inverse functions as well as the derivative of inverse trig functions.

In this video, we will do a few related rates examples! Don’t forget your differentiation techniques such as the chain rule and implicit differentiation. Make sure to do proper “bookkeeping” in order to not get lost in the details of the problem!

In this video, we will learn all about local and global minimums and maximums otherwise known as relative and absolute mins and maxs.

In this example video, we will go over the Mean Value Theorem as well as Rolle’s Theorem. Just make sure your conditions are met before you begin a problem!

In this video, we will go over examples dealing with what the first and second derivative tell us about the original function. Remember, the first derivative will relates to slope whereas the second derivative relates to concavity!

We are going to take everything learned in the previous video as well as everything learned about asymptotes and functions, put it all together, and graph some functions!

How do you optimize a problem? Hint: If we are trying to find a maximum or a minimum, what does that relate to? The first derivative!

In this video, we are going to use the derivative to help us approximate values that we would otherwise need a calculator to evaluate.

How do you take the limit of a functions that’s going towards infinity over infinity or zero over zero, or maybe some other difficult form? We will use L’Hopitals Rule to figure it out!

Newton’s Method is used to find the roots or zeroes of a function. What else can it be used for? Let’s take a look and see!

In this example video, we will learn a few basic rules for taking the antiderivative. Make sure to reviews derivatives before you start!

What is an integral? It’s the area under the curve! But before we find the exact values, we should learn how to estimate the area so that we understand the concept of the antiderivative.

Now that we know how to estimate the area, let’s look at what we can accomplish knowing the exact area before we dive into calculating it.

Now we will finally calculate integrals along a given interval. Let’s learn all about the Fundamental Theorem!

U-substitution allows us to reverse the chain rules and is one of the most common integration techniques! Learn more integration techniques in the Calculus 2 video series!