# Activities

• • • ##### Subject Area

• Math: Calculus: Derivatives
• Math: Calculus: Antiderivatives and Slope Fields

• ##### Author 9-12

90 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

CBL™/CBL 2™
TI Connectivity Cable

• ##### Report an Issue

Calculus with the TI-89

#### Activity Overview

In this Computer Algebra System (CAS) activity, students will explore the concept of limits of functions, and use CAS to demonstrate the definition of derivative.

#### Before the Activity

• Connect the CBR 2™ and CBL 2™ to the calculator
• Install TI Connect™ using the TI connectivity cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 6 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Explore the concept of the limit of a function f(x) as x approaches zero, infinity, or any other arbitrary value
• Investigate the horizontal and vertical asymptotes of a rational function; graphically, numerically, and symbolically
• Examine other important limits

• Use the CBL™/CBR™ to collect distance data
• Analyze the distance-time and velocity-time graphs using the calculator programs
• Find the relationship between distance and time graphs

• Understand that CAS can be used to demonstrate the definition of the derivative using the difference quotient
• Visualize the area under a curve using Riemann sums

• Model data using the logistic equation, study slopefields, and approximate the solution using Euler's method or the Runge-Kutta method
• Use the deSolve command to obtain an analytical solution
• #### After the Activity

Students answer questions on the Activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary