Exercise 1: Precise Definition of a Vector Function Limit https://youtu.be/mVJ4wviwDs8

In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st solution involves assuming the vector exists, and then using the basic definition of a vector function limit as well as the 3D distance formula, to prove the difference inequalities of the precise definition. The 2nd solution is the reverse: it involves assuming the precise definition difference inequalities and then working backwards to prove the vector function limit exists. Lastly, I show that the precise definition of a vector function limit in 3D can be visualized as a sphere which gets indefinitely smaller as the interval shrinks.

This is probably the only in-depth precise definition of limits for vector functions anywhere in the internet, so buckle up!

#math #vectorfunctions #limits #science #calculus

Limit of a Vector Function https://youtu.be/z48K6YRJ3Jc

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component functions. If the limit exists, then so does the limit of each component function.

#math  #limits #vectorfunctions #education #calculus

Creating Graphs of Sequences https://youtu.be/AEubaxYkfX4

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

Examples on Limits of Sequences https://youtu.be/80GBMrzuXVo

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

Squeeze Theorem for Sequences https://youtu.be/fmTDMMUL31Q

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.

Limit Laws for Sequences https://youtu.be/vgAitTQU2Fc

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.