An Elusive Limit Question 6: Subtracting Nearly Identical Numbers can BREAK Calculators! https://youtu.be/GEfzOVaPwAE

In this video I explain that the reason calculators gave an unclear limit for the complicated trigonometric function is because every term was nearly identical, to the point where subtracting them resulted in a difference too small for the precision of most calculators. 

An Elusive Limit Question 4-5: Evaluating the Limit using Taylor Series (and Wolfram Alpha) https://youtu.be/GEfzOVaPwAE

In this video I go over the earlier trigonometric (and inverse trigonometric) limit and solve it by writing the numerator and denominator as Taylor series. 

#math #science #education #calculus #WolframAlpha

An Elusive Limit Question 3: Using L'Hospital's Rule 7 Times in a Row (Using Wolfram Alpha) https://youtu.be/LRLahyO4SVk

In this video I go over the previous difficult trigonometric (and inverse trigonometric) function and this some apply L'Hospital's Rule to show that its limit as x approaches 0 is equal to 1.

Problems Plus 1: Tightly Packed Balls in a Box (and Tightly Packed Circles in a Square) https://youtu.be/Rs8YkurKjCM

In this video I determine the radius of 9 balls that are tightly packed inside a box. I first solve the 2D case by solving for the radius of 5 circles tightly packed inside a square.

Vectors and the Geometry of Space: Problems Plus https://youtu.be/4x6uh1zQ-M0

In this video I go over the end-of-chapter Problems Plus advanced math problems for the Vectors and Geometry of Space chapter. There are 8 problems in total and cover 3D geometry, surfaces, vectors, vector projections, and applications to physics and airplane dynamics. It's 4 hours of advanced math so buckle up!

Exercise 4: Approximating the Velocity of a Shallow Water Wave using Maclaurin Series https://youtu.be/Q_IXu-V8vng

In this video I go over the water wave velocity equation and approximate it when the waves are deep and when the waves are shallow.