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using Simpson's Rule with a partition having four intervals What degree of accuracy does this represent

Part I:

Begin Each Section with a Heading Text running in the wider column using traditional paragraphs and headings allows for two different kinds of access: scanning and reading When the narrative text relates to the Executive Summary on the same page, it s easy for a reader who is simply scanning the summary to read text that is of interest and skip or skim the rest A Subheading Here Breaks Up the Text Readers who are interested in the details will be able to get the information they seek by reading the text positioned in the wider column Your text can run for as many pages as needed You should aim to have about the same number of bulleted points on each page, just as you should try to have roughly the same quantity of text on each page Another Heading Indicates a New Section The narrative continues on from one page to the next as it would in a traditional one-column proposal This layout allows readers to read just the information they choose

Of course, there are many nuances that the preceding rules do not address, and special cases cause one or more rules to be violated But, in general, if you follow these rules, you will be creating resilient objects that are not easily misused

To better understand the how and why behind access control, a case study is useful One of the quintessential examples of object-oriented programming is a class that implements a stack As you probably know, a stack is a data structure that implements a last-in, first-out list Its name comes from the analogy of a stack of plates on a table The first plate on the table is the last one to be used A stack is a classic example of object-oriented programming because it combines storage for information along with the methods that access that information Thus, a stack is a data engine that enforces the last-in, first-out usage Such a combination is an excellent choice for a class in which the members that provide storage for the stack are private, and public methods provide access By encapsulating the underlying storage, it is not possible for code that uses the stack to access the elements out of order A stack defines two basic operations: push and pop A push puts a value onto the top of the stack A pop removes a value from the top of the stack Thus, a pop is consumptive; once a value has been popped off the stack, it has been removed and cannot be accessed again The example shown here creates a class called Stack that implements a stack The underlying storage for the stack is provided by a private array The push and pop operations are available through the public methods of the Stack class Thus, the public methods enforce the last-in, first-out mechanism As shown here, the Stack class stores characters, but the same mechanism could be used to store any type of data:

// A stack class for characters using System; class Stack { // These members are private char[] stck; // holds the stack int tos; // index of the top of the stack // Construct an empty Stack given its size public Stack(int size) { stck = new char[size]; // allocate memory for stack tos = 0; } // Push characters onto the stack public void Push(char ch) { if(tos==stckLength) { ConsoleWriteLine(" -- Stack is full"); return; } stck[tos] = ch; tos++; } // Pop a character from the stack

Of course this example is parallel to Example 830, and you should compare the two examples Our function is f ( x) = 1/( 1 + x 2 ) and our partition is P = {0, 1/4, 2/4, 3/4, 1} The sum from Simpson's Rule is S= 1/4 { f ( 0) + 4 f ( 1/4) + 2 f ( 1/2) + 4 f ( 3/4) + f ( 1) } 3 1 1 1 +4 2 12 1+0 1 + ( 1/4) 2 +2 1 1 1 +4 + 1 + ( 1/2) 2 1 + ( 3/4) 2 1 + 12

8: