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Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / BC, AB / BC Calc or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. AP Calculus AB covers basic introductions to limits, derivatives, and integrals.
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Advanced Placement (AP) [4] is a program in the United States and Canada created by the College Board. AP offers undergraduate university-level curricula and examinations to high school students. Colleges and universities in the US and elsewhere may grant placement and course credit to students who obtain qualifying scores on the examinations.
Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics
A cluster point or accumulation point of a sequence in a topological space is a point such that, for every neighbourhood of , there are infinitely many natural numbers such that . This definition of a cluster or accumulation point of a sequence generalizes to nets and filters .
His second proof was geometric. If () = and () =, the theorem can be written: + =.The figure on the right is a proof without words of this formula. Laisant does not discuss the hypotheses necessary to make this proof rigorous, but this can be proved if is just assumed to be strictly monotone (but not necessarily continuous, let alone differentiable).
The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in interest theory. Thus a(0)=1 and the value at time t is given by: = ().
Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the most common antiderivatives.
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