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Although Examplecs is quite short, it includes several key features that are common to all C# programs Let s closely examine each part of the program, beginning with its name The name of a C# program is arbitrary Unlike some computer languages (most notably, Java) in which the name of a program file is very important, this is not the case for C# You were told to call the sample program Examplecs so that the instructions for compiling and running the program would apply, but as far as C# is concerned, you could have called the file by another name For example, the preceding sample program could have been called Samplecs, Testcs, or even Xcs By convention, C# programs use the cs file extension, and this is a convention that you should follow Also, many programmers call a file by the name of the principal class defined within the file This is why the filename Examplecs was chosen Since the names of C# programs are arbitrary, names won t be specified for most of the sample programs in this book Just use names of your own choosing The program begins with the following lines:

/* This is a simple C# program Call this program Examplecs */

17 We do (a), (c), (e), and (g) (a) f g (x) = [(x + 1)2 ]2 2(x + 1)2 ; g f (x) = ([x 2 2x] + 1)2 2 (c) f g (x) = sin(cos(x 2 + x) cos (x 2 + x)) 2 g f (x) = cos(sin (x x 2 ) + sin(x x 2 )) 2 (e) f g (x) = sin(ln (x 2 + 2x) ln(x 2 + 2x)) 2 g f (x) = ln(sin (x 2 x) + 2 sin(x 2 x)) (g) f g (x) = [(2x 1)(x + 2)] [(2x 1)(x + 2) 1] [(2x 1)(x + 2) + 3] g f (x) = [2x(x 1)(x + 3) 1] [x(x 1)(x + 3) + 2] 18 We do (a), (c), (e), (g) (a) f is invertible, with f 1 (t) = (t 1)1/3 (c) h is invertible, with h 1 (t) = (sgn x) x 2 (e) h is invertible as long as we restrict the range to the positive real numbers Then the inverse is f 1 (t) = (1/3) ln t (g) f is not invertible because cot( /2) = cot(5 /2) = 0

This is a comment Like most other programming languages, C# lets you enter a remark into a program s source file The contents of a comment are ignored by the compiler Instead, a comment describes or explains the operation of the program to anyone who is reading its source code In this case, the comment describes the program and reminds you to call the source file Examplecs Of course, in real applications, comments generally explain how some part of the program works or what a specific feature does C# supports three styles of comments The one shown at the top of the program is called a multiline comment This type of comment must begin with /* and end with */ Anything between these two comment symbols is ignored by the compiler As the name suggests, a multiline comment can be several lines long The next line in the program is

using System;

Part I:

19 We will do (a), (c), (e), and (g)

This line indicates that the program is using the System namespace In C#, a namespace defines a declarative region Although we will examine namespaces in detail later in this book, a brief description is useful now Through the use of namespaces, it is possible to keep one set of names separate from another In essence, names declared in one namespace will not conflict with names declared in a different namespace The namespace used by the program is System, which is the namespace reserved for items associated with the NET Framework class library, which is the library used by C# The using keyword simply states that the program is using the names in the given namespace (As a point of interest, it is also possible to create your own namespaces, which is especially helpful for large projects) The next line of code in the program is shown here:

class Example {

This line uses the keyword class to declare that a new class is being defined As mentioned, the class is C# s basic unit of encapsulation Example is the name of the class The class definition begins with the opening curly brace ({) and ends with the closing curly brace (}) The elements between the two braces are members of the class For the moment, don t worry too much about the details of a class except to note that in C#, most program activity occurs within one The next line in the program is the single-line comment, shown here:

(g) Not invertible 20 We will do (a), (c), (e), and (g) (a) Invertible, f 1 (t) = 3 t 1 (c) Invertible, h 1 (t) = cos (t) 1 1 (e) Invertible, g (t) = cot (t) 1 1 + 4t (g) Invertible, f 1 (t) = 2

// A C# program begins with a call to Main()

.