Multivariable calculus (also known as multivariate calculus ) is the extension of calculus in one variable to calculus with functions of several variables : the differentiation and integration of functions involving multiple variables, rather than just one. [1]

A study of limits and continuity in multivariable calculus yields many counter-intuitive results not demonstrated by single-variable functions. [1] : 19–22 For example, there are scalar functions of two variables with points in their domain which give a particular limit when approached along any arbitrary line, yet give a different limit when approached along a parabola .

approaches zero along any line through the origin. However, when the origin is approached along a parabola y = x 2 {\displaystyle y=x^{2}} , it has a limit of 0.5. Since taking different paths toward the same point yields different values for the limit, the limit does not exist.

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