Activity Overview
In this activity, students investigate and learn about functions known as sequences. They learn how they can be represented symbolically, graphically, and numerically.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 79 - 86 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Investigating Sequences Numerically, Graphically and Symbolically:
Use the seq (sequence) command to look at the sequence numerically
Graph the sequence to examine its behavior and use the limit command to evaluate the sequence symbolically
Convergence of an Infinite Series:
Use the ratio test to establish the convergence of the infinite series
Enter the expression for the n th partial sum and observe values in a table
Estimate the sum of the infinite series
Taylor Series:
Define the functions f(x) and p(x)
Equate the first and second order derivatives to calculate the coefficient of P(x)
Graph the 2 functions
Generate the polynomial using the Taylor command
Integral of Taylor Polynomial:
use the taylor command and observe two results
After the Activity
Students will complete the practice exercise problems.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary