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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_558</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_557.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_558</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_559.html">next page ></a></td> </tr> <tr> <td align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 558</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Courier New, Courier, Mono New, Courier, Mono" size="2">{<br />聽聽聽聽聽return聽Funct(leftEdge聽+聽width聽/聽2.0)聽*聽width;<br />}<br /><br />//******************************************************************<br /><br />float聽Funct(聽/*聽in聽*/聽float聽x聽)聽聽聽//聽Value聽to聽be聽cubed<br /><br />//聽Computes聽x聽cubed.聽You聽may聽replace聽this聽function聽with聽any<br />//聽single-variable聽function<br /><br />//聽Precondition:<br />//聽聽聽聽聽The聽absolute聽value聽of聽x聽cubed聽does聽not聽exceed聽the<br />//聽聽聽聽聽machine's聽maximum聽float聽value<br />//聽Postcondition:<br />//聽聽聽聽聽Function聽value聽==聽x聽cubed<br /><br />{<br />聽聽聽聽return聽x聽*聽x聽*聽x;<br />}</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Testing: We should test this program with sets of data that include positive, negative, and zero values. It is especially important to try to input values of 0 and 1 for the number of divisions. The results from the program should be compared against values calculated by hand using the same algorithm and against the true value of the area under the curve of X</font><font face="Times New Roman, Times, Serif" size="2"><sup>3</sup></font><font face="Times New Roman, Times, Serif" size="3">, which is given by the formula</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="ebbaf99f8950808713e06c1ceb2f5d5d.gif" border="0" alt="0558-01.gif" width="116" height="32" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">(This formula comes from the mathematical topic of calculus. What we have been referring to as the area under the curve in the interval </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">a</font><font face="Times New Roman, Times, Serif" size="3"> to </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">b</font><font face="Times New Roman, Times, Serif" size="3"> is called the <i>integral</i> of the function from </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">a</font><font face="Times New Roman, Times, Serif" size="3"> to </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">b</font><font face="Times New Roman, Times, Serif" size="3">.)</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Let's consider for a moment the effects of representational error on this program. The user specifies the low and high values of the interval, as well as the number of subdivisions to be used in computing the result. The more subdivisions used, the more accurate the result should be because the rectangles are narrower and thus approximate more closely the shape of the area under the curve. It seems that we can obtain precise results by using a large number of subdivisions. In fact, however, there is a point beyond which an increase in the number of subdivisions <i>decreases</i> the precision of the results. If we specify too many subdivisions, the area of an individual rectangle becomes so small that the computer can no longer represent its value accurately. Adding all those inaccurate values produces a total area that has an even greater error.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_557.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_558</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_559.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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