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(d) Since limx + sin x does not exist, l H opital s Rule does not apply In fact the requested limit does not exist (e) It is convenient to rewrite this limit as x2 x x e lim Since limx x 2 = limx e x = , l H opital s Rule applies Thus x2 2x = lim x x x e x e lim A final application of l H opital s Ruleshows that this last limit is lim

14:

As the output confirms, each time a key is pressed, ReadKey( ) immediately returns the keypress As explained, this differs from Read( ) and ReadLine( ), which use line-buffered input Therefore, if you want to achieve interactive responses from the keyboard, use ReadKey( )

ConsoleOut and ConsoleError are objects of type TextWriter Console output is most easily accomplished with Write( ) and WriteLine( ), with which you are already familiar Versions of these methods exist that output each of the built-in types Console defines its own versions of Write( ) and WriteLine( ) so they can be called directly on Console, as you have been doing throughout this book However, you can invoke these (and other) methods on the TextWriter that underlies ConsoleOut and ConsoleError, if you choose Here is a program that demonstrates writing to ConsoleOut and ConsoleError By default, both write to the console

// Write to ConsoleOut and ConsoleError using System; class ErrOut { static void Main() { int a=10, b=0; int result; ConsoleOutWriteLine("This will generate an exception"); try { result = a / b; // generate an exception } catch(DivideByZeroException exc) { ConsoleErrorWriteLine(excMessage); } } }

x

The output from the program is shown here:

Sometimes newcomers to programming are confused about when to use ConsoleError Since both ConsoleOut and ConsoleError default to writing their output to the console, why are there two different streams The answer lies in the fact that the standard streams can be redirected to other devices For example, ConsoleError can be redirected to write to a disk file, rather than the screen Thus, it is possible to direct error output to a log file, for example, without affecting console output Conversely, if console output is redirected and error output is not, then error messages will appear on the console, where they can be seen We will examine redirection later, after file I/O has been described

My analysis used proprietary stochastic simulation techniques (see attached)

Part I:

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The NET Framework provides classes that allow you to read and write files Of course, the most common type of files are disk files At the operating system level, all files are byte oriented As you would expect, there are methods to read and write bytes from and to a file Thus, reading and writing files using byte streams is very common You can also wrap a byte-oriented file stream within a character-based object Character-based file operations are useful when text is being stored Character streams are discussed later in this chapter Byteoriented I/O is described here To create a byte-oriented stream attached to a file, you will use the FileStream class FileStream is derived from Stream and contains all of Stream s functionality Remember, the stream classes, including FileStream, are defined in SystemIO Thus, you will usually include

using SystemIO;

To create a byte stream linked to a file, create a FileStream object FileStream defines several constructors Perhaps its most commonly used one is shown here: FileStream(string path, FileMode mode) Here, path specifies the name of the file to open, which can include a full path specification The mode parameter specifies how the file will be opened It must be one of the values defined by the FileMode enumeration These values are shown in Table 14-4 In general, this constructor opens a file for read/write access The exception is when the file is opened using FileModeAppend In this case, the file is write-only If a failure occurs when attempting to open the file, an exception will be thrown If the file cannot be opened because it does not exist, FileNotFoundException will be thrown If the file cannot be opened because of some type of I/O error, IOException will be thrown Other exceptions include ArgumentNullException (the filename is null), ArgumentException (the filename is invalid), ArgumentOutOfRangeException (the mode is invalid), SecurityException (user does not have access rights), PathTooLongException (the

Value FileModeAppend FileModeCreate FileModeCreateNew FileModeOpen FileModeOpenOrCreate FileModeTruncate