Standard #: MA.912.C.1.6


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Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.


Examples


Example: Where does the function, begin mathsize 12px style f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator x squared minus 7 x plus 10 to the power of comma end fraction end style, have asymptote(s)?

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Resources

Lesson Plan

Name Description
Leap Frog Review Game

In this lesson students will demonstrate their knowledge of limits, graphing, and exact trig limits evaluated using substitution. The students will play a game in which they evaluate their knowledge of problems in the unit while it serves as a formative assessment for the teacher. The students receive immediate feedback on their work while the teacher works the problems, correcting errors or misconceptions. This lesson gives the student a power review of the concepts in the unit because the timing is determined by the teacher. All students are engaged and focused while playing this game. Giving students access to the PowerPoint of the game after the lesson provides a good study tool for the students.

Perspectives Video: Professional/Enthusiast

Name Description
Asymptotic Behavior in Shark Growth Research

Fishery Scientist from Florida State University discusses his new research in deep sea sharks and the unusual behavior that is found when the data is graphed.

Download the CPALMS Perspectives video student note taking guide.

Text Resource

Name Description
No Limits For Usain

This informational text resource is intended to support reading in the content area. The text uses the story of Usain Bolt and his quest to reduce his world record in the 100 meter race to raise the question of whether there is a limit to his—or any human's—athleticism. The article uses number series, limits, and convergent and divergent series to prove that, hypothetically at least, a world record will go on reducing beyond any limit. A logistic curve is shown to model the data.

Tutorials

Name Description
More Limits at Infinity

Here we will explore three more functions, and find their limits as they approach infinity.

Limits with Two Horizontal Asymptotes

Here we will find the limit of a function as it approaches positive and negative infinity and results in two horizontal asymptotes.

Student Resources

Tutorials

Name Description
More Limits at Infinity:

Here we will explore three more functions, and find their limits as they approach infinity.

Limits with Two Horizontal Asymptotes:

Here we will find the limit of a function as it approaches positive and negative infinity and results in two horizontal asymptotes.



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