Activity Detail
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Differential Equations and Slope Fields
 


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

    		Other Downloads




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    Subject Area:
    Math : Calculus : Applications of Integral, Antiderivatives and Definite Integrals

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    60 Minutes

    Device:
    TI-89 / TI-89 Titanium

    Apps:
     

    Software:
     

    Accessories:
     

    Other:
    This is Activity 9 from the EXPLORATIONS Book:
    Advanced Placement Calculus with the TI-89.

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