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Using the same philosophy about odd exponents as we did with sines and cosines, we substitute sec2 x 1 for tan2 x The result is tan x( sec2 x 1) sec3 x dx We may regroup the terms in the integrand to obtain [sec4 x sec2 x] sec x tan x dx A u-substitution suggests itself: We let u = sec x and therefore du = sec x tan x dx Thus our integral becomes u4 u2 du = Resubstituting the value of u gives tan3 x sec3 x dx = sec3 x sec5 x + C 5 3 u3 u5 + C 5 3

Queue<T> is the generic equivalent of the non-generic Queue class It supports a first-in, first-out list Queue<T> implements the ICollection, IEnumerable, and IEnumerable<T> interfaces Queue<T> directly implements the Clear( ), Contains( ), and CopyTo( ) methods defined by ICollection<T> (The Add( ) and Remove( ) methods are not supported, nor is the IsReadOnly property) Queue<T> is a dynamic collection that grows as needed to accommodate the elements it must store It defines the following constructors: public Queue( ) public Queue(int capacity) public Queue(IEnumerable<T> collection) The first form creates an empty queue with an initial default capacity The second form creates an empty queue with the initial capacity specified by capacity The third form creates a queue that contains the elements of the collection specified by collection In addition to the methods defined by the interfaces that it implements (and those methods defined by ICollection<T> that it implements on its own), Queue<T> defines the methods shown in Table 25-21 Queue<T> works just like its non-generic counterpart To put an object in the queue, call Enqueue( ) To remove and return the object at the front of the queue, call Dequeue( ) You can use Peek( ) to return, but not remove, the next object An InvalidOperationException is thrown if you call Dequeue( ) or Peek( ) when the invoking queue is empty

ful to avoid euphemisms and long words In other words, my writing got better by my learning the correct level of proo ng Level One proo ng usually includes the following: 1 Can your readers easily understand what you re asking them to do 2 If 100 percent of your readers aren t familiar with your technical terms and industry jargon, have you de ned them 3 If 100 percent of your readers aren t familiar with your acronyms, have you explained them 4 Have you con rmed that all numbers included in your communication are correct 5 Have you avoided long or complicated sentences and sentence fragments (explained in Five) 6 Are you certain that you ve maintained noun/pronoun and subject/verb agreement (explained in Seven) 7 Is your punctuation correct 8 Are words capitalized properly 9 Have you used your spell checker 10 Have you reread your communication to catch missing words or phrases

Part II:

Method public T Dequeue( ) public void Enqueue(T item) public T Peek( ) public T[ ] ToArray( ) public void TrimExcess( )

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TABLE 25-21

Description Returns the object at the front of the invoking queue The object is removed in the process Adds item to the end of the queue Returns the object at the front of the invoking queue, but does not remove it Returns an array that contains copies of the elements of the invoking queue Removes the excess capacity of the invoking stack

Here is an example that demonstrates Queue<T>:

// Demonstrate the Queue<T> class using System; using SystemCollectionsGeneric; class GenQueueDemo { static void Main() { Queue<double> q = new Queue<double>(); qEnqueue(986); qEnqueue(2120); qEnqueue(320); qEnqueue(31416); double sum = 00; ConsoleWrite("Queue contents: "); while(qCount > 0) { double val = qDequeue(); ConsoleWrite(val + " "); sum += val; } ConsoleWriteLine("\nTotal is " + sum); } }

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The output is shown here:

HashSet<T> supports a collection that implements a set It uses a hash table for storage HashSet<T> implements the ICollection<T>, ISet<T>, IEnumerable, IEnumerable<T>, ISerializable, and IDeserializationCallback interfaces HashSet<T> implements a set in which all elements are unique In other words, duplicates are not allowed The order of the elements is not specified HashSet<T> implements the full complement of set operations defined by ISet<T>, such as intersection, union, and symmetric difference This makes