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In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. [1] Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals .
Learn what limits are and how to evaluate them using examples and graphs. Find out how to approach infinity, one-sided limits, and indeterminate forms.
Learn what limits are and how they describe how a function behaves near a point. See examples, graphs, notation and problems with limits.
Limits in maths are defined as the values that a function approaches the output for the given input values. Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity.
Learning Objectives. Using correct notation, describe the limit of a function. Use a table of values to estimate the limit of a function or to identify when the limit does not exist. Use a graph to estimate the limit of a function or to identify when the limit does not exist. Define one-sided limits and provide examples.
With limits, we can accomplish seemingly impossible mathematical things, like adding up an infinite number of numbers (and not get infinity) and finding the slope of a line between two points, where the "two points'' are actually the same point.
The idea of a limit is central to all of calculus. We begin this chapter by examining why limits are so important. Then, we go on to describe how to find the limit of a function at a given point.
