Titlebook: Calculus I; Brian Knight,Roger Adams Book 1975 Springer Science+Business Media New York 1975 curve sketching.differential equation.integra

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Curve Sketching,erations which may give us a very good idea of the general form of a graph, without our having to plot it point by point. We enumerate below some of the more important of these features to look for in an equation, and illustrate in the examples how the graph may be built up from them. Not all of the

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,Newton’s Method, equations:.have roots which we may estimate, by graphing the functions and finding where the graphs cut the .-axis, but which we cannot find exactly. In these cases a numerical procedure known as Newton’s method allows us to use a value .. which is an approximate root of the equation:.in order to o

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Substitution in Integrals,e. In fact the rule given in Chapter 12 is a special case of a more general rule for substituting in integrals. In the method of substitution, we try to reduce a given integral to one of the standard types by picking out a likely expression in . which we call .(.), and then expressing the whole inte

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Book 1975ctions A set is a collection of distinct objects. The objects be­ longing to a set are the elements (or members) of the set. Although the definition of a set given here refers to objects, we shall in fact take objects to be numbers throughout this book, i.e. we are concerned with sets of numbers. Il

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