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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