calc - Limits and Continuity of Functions of Two or More...

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Limits and Continuity of Functions of Two or More Variables Introduction Recall that for a function of one variable, the mathematical statement means that for x close enough to c, the difference between f(x) and L is "small". Very similar definitions exist for functions of two or more variables; however, as you can imagine, if we have a function of two or more independent variables, some complications can arise in the computation and interpretation of limits. Once we have a notion of limits of functions of two variables we can discuss concepts such as continuity and derivatives . Limits The following definition and results can be easily generalized to functions of more than two variables. Let f be a function of two variables that is defined in some circular region around (x_0,y_0). The limit of f as x approaches (x_0,y_0) equals L if and only if for every epsilon>0 there exists a delta>0 such that f satisfies whenever the distance between (x,y) and (x_0,y_0) satisfies We will of course use the natural notation
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calc - Limits and Continuity of Functions of Two or More...

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