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Applications of differentiation,ome from the standard functions, calculus gives us a straightforward technique for solving these problems. We use the first and second derivatives to help decide whether a function is increasing or decreasing and to determine the shape of the curve.

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Line integrals, two or three variables. When the domain of such functions is a region of a space, we usually refer to the functions as .. Thus, a vector field is a rule which associates a vector with each point in a region of space. In this usage, we could refer to a function of two or three variables as a ..

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https://doi.org/10.1007/978-981-287-527-3 to develop these skills. Most of the ideas will be familiar but there may be some ‘tricks of the trade’ which are new to you. You should be aware that we are working with exact numbers and algebraic expressions. None of the exercises need a calculator and using one may obscure the point being covered.

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Preliminaries, to develop these skills. Most of the ideas will be familiar but there may be some ‘tricks of the trade’ which are new to you. You should be aware that we are working with exact numbers and algebraic expressions. None of the exercises need a calculator and using one may obscure the point being covered.

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Functions of two variables, of a function of one variable, we define a function . of two variables, . and ., say, by its value at all points of the domain. Thus the domain has to be described in terms of both variables . and .. The following definition enables us to do this.

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