Cubic Formula Proof Step 5: Putting it All Together to Solve for x https://youtu.be/ZpYMkiRIbkU - summary - playlist - notes

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 method in Microsoft OneNote, I may be the first person to show the complete solution being derived in real-time!

#math #science #education #algebra #STEM

Introduction to Infinite Sequences and Series https://youtu.be/dhBcdt4-N4c - summary - playlist - notes

In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.

#math #science #education #calculus #STEM

Sequences: Definition, Notation, Fibonacci, and Examples https://youtu.be/jlDvjip0hLk - summary - playlist - notes

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. I also discuss briefly discuss the famous Fibonacci sequence, which is defined recursively by adding up the previous two terms.

#math #science #education #algebra #STEM

The Limit of a Sequence https://youtu.be/NANqzQ_ZirM - 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.

#math #science #education #algebra #maths

The Precise Definition of a Limit of a Sequence https://youtu.be/baF4w9MeCiM - summary - playlist - notes

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 number ε such that it has a corresponding number N where if the sequence term n is greater than N, then the absolute value of the difference between the n-th term of the sequence and the limit L is less than ε.

#math #science #education #algebra #sequences

Infinite Limits of Sequences at Infinity https://youtu.be/a4M4w3PhCd8 - summary - playlist - notes

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.

#math #science #education #algebra #sequences

Limit Laws for Sequences https://youtu.be/vgAitTQU2Fc - summary - playlist - notes

In this video I list the main limit laws for sequences, and which are just the general limit laws since they hold for convergent sequences as well.

#math #science #education #limits #sequences

Squeeze Theorem for Sequences https://youtu.be/fmTDMMUL31Q - summary - playlist - notes

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 have the same limit, then our given sequence also has that same limit, and is said it gets "squeezed" between the two sequences.

#math #science #education #limits #sequences

Examples on Limits of Sequences https://youtu.be/80GBMrzuXVo - summary - playlist - notes

In this video I go over 4 examples on the limits of sequences and on determining if the limits exists or the sequence diverges.

#math #science #education #limits #sequences

Plugging a Sequence into a Function and Examples https://youtu.be/5Vc8QX_I7KA - summary - playlist - notes

In this video I go over Theorem 3, which states that if a sequence has a limit, then plugging it into a continuous function at that limit is the same as plugging in the limit.

#math #science #education #limits #sequences

Creating Graphs of Sequences https://youtu.be/AEubaxYkfX4 - summary - playlist - notes

In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator.

#math #science #Desmos #limits #sequences