# Limit of a function (lesson)

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Note: For full lesson w/lab questions, open the attached document)

Synopsis
Students work in teams to explore the definition of a limit.

Main Standard
MA8.0 Students are familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether certain sequences converge or diverge.

Materials
Graphing Calculators
Copies, Limit of a Function

Teacher Directions

Pass out Limit of a Function. Have students work on the first page in teams. Student teams should have a slightly difficult time with Part I as it is a difficult definition to understand. When you feel student teams have had a chance to brainstorm answers, stop the class and have teams share answers. The definition may not be perfectly clear even after the discussion, but should become clearer as they work through the next parts.

Part II of the activity sheet has students work on the part of the definition “as x approaches c”. Make sure in this part they eventually pick x-values VERY close to 0. Also, students may need help with how to set their calculator to the ask mode. It is important that they understand that in the definition “L” is the y-value that they are approaching. Make sure to summarize their work once you feel most teams have completed Part II.

Part III, encourage them to make number lines and/or tables to show the limiting process for the x-value to deduce the “L”. Problems A-E takes them through various scenarios of types of functions. The last question asks them to deduce under what conditions they think the limit does not exist.