Let f be continuous and let Bg be the ball of radius ɛ centered at the point (xo, yo, zo). Let vol (Be) be the volume of Be. Prove that 1 lim E→0 vol ( B) Г(х, у. 2) dV %3D f (х0. Уo. 20).

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: