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In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after ...
Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis" is commonly used for advanced parts. Analysis is further subdivided into real analysis , where variables represent real numbers , and complex analysis , where variables represent complex numbers .
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
Advanced. Specialized. Miscellaneous. v. t. e. In integral calculus, the tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of into an ordinary rational function of by setting . This is the one-dimensional stereographic projection of the unit ...
Miscellaneous. v. t. e. 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 ( multivariate ), rather than just one. [1]
Solution by calculus. In the present day, this problem is widely known because it appears as an exercise in many first-year calculus textbooks (for example that of Stewart ). Let a = the height of the bottom of the painting above eye level; b = the height of the top of the painting above eye level; x = the viewer's distance from the wall;
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