Exercise 2: Properties of Vector Function Limits https://youtu.be/y5e8Xhdt39Q 

In this video I prove the main properties of vector function limits, namely the addition, constant multiplication, as well as the dot and cross products of their limits.

#math #vectorfunctions #limits #science #calculus

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

Example 5: Vector and Parametric Equations of a Line Segment https://youtu.be/dSIfPYi3q4U

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 parameter t between 0 and 1.

#math #vectorfunctions #geogebra  #science #calculus

Plane Curves as Vector Functions and the Structure of a DNA Helix https://youtu.be/S94nUYS8Imc

In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix.

#math #vectorfunctions #planecurves #biology #calculus

Space Curves: Tracing out the Tip of a Continuous Vector Function https://youtu.be/DHJnsmyG1LQ

In this video I show that a continuous vector function in 3D forms a curve in space when tracing out the point on the tip of the vector as it moves in time.

#math #vectofunctions #spacecurves #education #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