# Nonexistence of a Multivariable Limit

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In multivariable calculus, a limit of a function exists at a point if and only if we can make as close as we want to for all points arbitrarily close to One way to show that a limit does not exist (i.e. the definition fails) is to show that the function approaches different values from different directions. Akin to the notion of a one-sided limit in single-variable calculus, we consider the limit along a path in multivariable calculus. If the limit exists and is the same along all paths to then the limit of the function exists.

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Contributed by: Laura R. Lynch (May 2014)

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