Limits
Definition
Limits are used in calculus to describe the behavior of a function as it approaches a certain value or point. It helps determine what happens to the output of a function when the input gets closer and closer to a specific value.
Analogy
Imagine you're trying to reach the top floor of a building, but there's an elevator that only goes up one floor at a time. The limit is like standing on each floor and seeing how close you can get to the top without actually reaching it.
Related terms
Derivative: The derivative measures how fast a function is changing at any given point.
Continuity: Continuity refers to whether or not there are any breaks, holes, or jumps in a function.
Infinitesimal: An infinitesimal is an extremely small quantity that approaches zero but is not exactly zero. It plays an important role in calculus when dealing with limits and derivatives.
"Limits" appears in:
Study guides (3)
Additional resources (4)
Practice Questions (8)
- Which rates of change depend on the concept of limits?
- Which property of limits is used to evaluate the following limit? lim(x→3) (4x^2 - 7x)
- Which representation of limits is the most common method used to determine limits?
- Which representation of limits is useful to understand the behavior of a function when working with abstract equations?
- Which representation of limits involves creating a table of values with x-values close to the limit and observing what the y-values of the function approach?
- Which representation of limits involves analyzing the function behavior as x approaches positive or negative infinity?
- Which representation of limits is particularly useful when dealing with functions that have vertical asymptotes or removable discontinuities?
- Which representation of limits involves using tables, graphs, and equations simultaneously to analyze the behavior of a function?
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