MATH114 Chapter Notes - Chapter 5.1: Opata Language

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MATH114 Full Course Notes
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MATH114 Full Course Notes
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For {ai} a set of numbers indexed by the integers, and for integers m n we have ai = am + am+1 + + an 1 + an. n(cid:88) i=m n(cid:88) Riemann sums, approximate area under a curve, approximate distance: X f (a + i x), where x = (b a)/n. i=1. If f is a velocity function then sn can be used to approximate the distance traveled during the interval of time from t = a to t = b. When n is increased the number of rectangles used is increased and the approximation is improved. If we let n go to in nity then the approximation becomes the true area under the curve. The de nite integral of the function f over the interval [a, b] is the limit as n goes to in nity of the riemann sum sn of f (x) on [a, b].

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