limits

** AP CALCULUS **
 * LOIS MOYE **
 * Pamlico County High School **

The Limit of a Function

North Carolina Standard Course of Study Competency Goal 1: The learner will demonstrate an understanding of the behavior of functions Objectives 1.01 Demonstrate an understanding of limits, both local and global a. Calcululate limits, including one sided, using algebra b. Estimate limits from graphs or tables of data.

Objective: The learner will evaluate limits using graphic and numeric methods. The learner will create a product consisting of three function to illustrate the graphic method of solving a limit.

Blast from the Past: Remember Geometric Series??? Write a geometric series with a common ratio, r, such that 0<r<1. As the number of terms increases, a. Each term "gets closer" to what number? b. The sum "approaches" what number?

Instruction: Let's investigate the behavior of a function as x approaches any particular number, a. ( What happens to y, when x gets really close to a) We will use applets to demonstrate behavior of following function types: A. [|linear function investigation]

B. [|jumps, vertical asymptote, wiggly function]

C. [|limits at infinity]

**Guided Practice:** Use the link to go to the National Curve Bank and answer the questions about the three very sweet curves [|Guided Practice Limit Exercise]

**Independent Practice** Download the Graphical Approach to Limits Worksheet (Stu Schwartz) Look at the classwork examples 1,2 and 6. Use the google form to find the limits. [|google form]

Complete the Classwork Section 1 - 18 for homework.

**Collaboration:** Groups of three. Product: You will create a word document similar to your guided practice exercise with three graphs and limit questions. Each person in the group will create their own graph using TI Interactive or TI connect, and equation editor. and then develop at least six limits associated with that graph. One graph must be a piecewise function. The second must be trigonometric. The third graph must be a rational function with a vertical asymptote and a horizontal asymptote. Check each others creativity and correctness. Put together the three pieces of work into one document, save your product on a flashdrive or email your work to me.

Just in case you may need a little bit extra help check out the video tutorials... [|Brightstorm Tutorials]

Just in case you need a little credit, post a note on wallwisher... [|wallwisher limits]