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In mathematics, Minkowski's question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. [1] It maps quadratic irrational numbers to rational numbers on the unit interval , via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the ...
Minkowski's question mark function: Derivatives vanish on the rationals. Weierstrass function: is an example of continuous function that is nowhere differentiable;
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
The question mark'? ' (also known as interrogation point, query, or eroteme in journalism [1]) is a punctuation mark that indicates a question or interrogative clause or phrase in many languages. History
In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context.
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.