Here we prove a multivariable limit exists using the definition.

The definition of a limit is:

Let epsilon be larger than zero. Then the real number L is called the limit of the function f(x,y) at (a,b) if there is a real number delta larger than zero, such that the when the distance from (x,y) to (a,b) is less then delta we are guaranteed that |f(x,y) - L| will be less than epsilon.

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