• In this section, the limit is described, examples of limits are given, as well as rules governing limits of functions that are added, subtracted, multiplied, divided, and raised to a power.

• The limit is used in the estimation of infinite sums and the definition of the derivative in calculus.

• In general, the limit is used to describe *closeness* of a function to a value when the exact value cannot be identified.

• If the Lim_{x→a}f(x) = L, then it is said that the function f(x) gets close to and may equal some number L as x approaches and gets close to some number *a*.

• For example, consider the function:

f(x) = x

^{2}+ 2

What will the value of f(x) be close to when ...

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