In this video I derive the parametric equations of a trochoid, which is the shape obtained by tracing a point as a circle rotates. If the point traced is on the circle itself, then the shape is the famous

In this video I derive the parametric equations of a trochoid, which is the shape obtained by tracing a point as a circle rotates. If the point traced is on the circle itself, then the shape is the famous

In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I also plot the trefoil knot in 3D using the amazing GeoGebra graphing calculator

A math guide on graphing linear equations.

In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first recap on the vector equation of a line segment, which involves a

In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator. I also go over an example on finding the values of r in r^n that are convergent and plot them

In this video I rewrite the general squeeze theorem into its equivalent form for sequences. Essentially, if a sequence is always between two other sequences after a given set of terms, and those two sequences

In this video I go over the notation and precise definition for sequences that diverge to infinity when the number of terms go to infinity. The precise definition states that the limit of a sequence approaches

In this video I go over a more precise definition of the limit of a sequence by using the same approach as for the limit of a function. If the limit of a sequence exists, then there must be a positive

In this video I go over a more precise definition of the limit of a sequence by using the same approach as for the limit of a function. If the limit of a sequence exists, then there must be a positive

In this video I go over the limit of a sequence, its notation, as well as plotting it on a number line and graphing it out. - summary - playlist - notes

In this video I go over the limit of a sequence, its notation, as well as plotting it on a number line and graphing it out. A sequence is a list of numbers of definite order whose domain is the set of

In this video I go over sequences, which are just ordered lists of numbers, the notation used to describe them, and several examples to illustrate how to obtain the general formula of the terms of a sequence.

In this video I go over sequences, which are just ordered lists of numbers, the notation used to describe them, and several examples to illustrate how to obtain the general formula of the terms of a sequence.

In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. Because I used the copy and paste

In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. The first solution of x is obtained

In this video I go over the fourth step of the Cubic Formula proof which involves obtaining the complex solutions of y by considering the cube root of unity. Since the cube root of the z values from Vieta's

In this video I demonstrate that the square root of 1 (or unity) has two solutions while the cube root of unity has three solutions, two of which are rotations in the complex plane. I show this by first

In this video I demonstrate that the square root of 1 (or unity) has two solutions while the cube root of unity has three solutions, two of which are rotations in the complex plane. I show this by first

In this video I go over the third step of the Cubic Formula proof which involves plugging our z value back into Vieta's substitution to obtain our first y solution. Recall that in Step 1 we removed the