Standard #: MAFS.912.C.1.1 (Archived Standard)


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Understand the concept of limit and estimate limits from graphs and tables of values.


Remarks


Example 1: For , estimate   by calculating the function's values for x = 2.1, 2.01, 2.001 and for x = 1.9, 1.99, 1.999. Explain your answer.

Example 2: A dog started to chase Kathy from 100 meters away. The dog runs fast so that every minute, the distance between Kathy and the dog is halved. Make a graph that shows the distance between Kathy and the dog in meters versus the time in minutes. Write a function to determine the distance between Kathy and the dog at any given time. Will the dog ever catch Kathy? Write a statement about the distance between Kathy and the dog as the time increases.

Example 3: A skydiver free falls from an airplane. The following graph shows the velocity of the skydiver. The air resistance and the gravity are the two forces that affect the velocity of a falling object. Write a paragraph that explains the graph, including but not limited to how the velocity of the skydiver changes as the time increases. You might read about the concept of terminal velocity to make an accurate explanation of the graph.



General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Limits and Continuity - Develop an understanding of the concept of limit by estimating limits graphically and numerically and evaluating limits analytically. Extend the idea of a limit to one-sided limits and limits at infinity. Use limits to define and understand the concept of continuity, decide whether a function is continuous at a point, and find types of discontinuities. Understand and apply continuity theorems.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

Course Number1111 Course Title222
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Resources

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
Limit and Function Defined at Point of Discontinuity

In this video we will determine if a limit exists at a point of discontinuity.

Limits and Infinity

We will look at examples of limits at infinity.

Introduction to limits

This video will provide an introduction to the intuition behind limits through graphing.

Two-sided limit from a graph

Determine the limit of a function from the left and from the right of an x-value from graph.

Student Resources

Tutorials

Name Description
Limit and Function Defined at Point of Discontinuity:

In this video we will determine if a limit exists at a point of discontinuity.

Limits and Infinity:

We will look at examples of limits at infinity.

Introduction to limits:

This video will provide an introduction to the intuition behind limits through graphing.

Two-sided limit from a graph:

Determine the limit of a function from the left and from the right of an x-value from graph.



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