By P.M. Dew, James

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810930 49 Basic Mathematics and Applications 1. 39E+OO * ! 5) We have not attempted to evaluate [(1) in our program; the result would be a runtime failure. From the table of values, however, it appears that f(x) 'tends to' a definite value asx 'tends to' 1. We conjecture that the limiting value is 1. We say that f(x) has a limit of 1 at x = 1, and we write lim f(x) = 1 x-+ 1 It is important to understand that we cannot claim to have proved this by examining computer outputt. The reader is advised to consult a textbook on analysis for further information (see reading list at the end of this chapter).

A library in Pascal is a program. g. g. array types>

Simple Simon We now consider the general principles we should bear in mind when developing mathematical software, with particular reference to the structure and design of the mathlib library. In developing any piece of software we should be guided by the principles of good programming practice, and much of what is said here is simply the procedure we should aim to follow whenever we write a program. The process of producing mathematical software involves (i) (ii) (iii) (iv) (v) Design and analysis of algorithms; Coding the algorithms (software realisation); Extensive testing; Detailed documentation; Distribution and maintenance of the software.