Slopes of Secant and Tangent Lines in Mathematica

How quickly is this barrel draining? Let's figure it out by looking at average rates of change.
In this video, I use Mathematica to help us tackle secant lines. I use TableForm[] function and ListPlot[] to get a good picture of what is happening.

00:42 - Part (a) Slopes of Secant Lines
04:48 - Part (b) Averaging Slopes
05:25 - Part (c) Plot the Results

WHAT ELSE YOU NEED TO KNOW:
1. What is a Limit? An Example in Mathematica:

2. Limits from the Left and Right:

3. Solving Limits with Algebra:

4. What is the Limit of Sin(x)/x as x Approaches Zero? Limits in Excel:

YOU MAY FIND THIS INTERESTING:
1. Solving Differential Equations in Mathematica:

2. Find the Equation of a Tangent Line:

3. How Fast is the Object Traveling when It Hits the Ground?

Hey! I’m Dr. John Estes, Associate Professor of Mathematics at Belhaven University. I have been teaching mathematics professionally since 2008, and I love helping students understand the wonderful world of mathematics more.
I’ve made these videos as a resource for students, and I hope they help you with your studies.
Thanks for watching! SUBSCRIBE for updates and connect with me on Facebook!
---------------------------------------------------------------------------------------------------------------------------------------------------------