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		p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" align="left">b>
		font face="Verdana" size="6">Holistic Numerical Methods Institute/font>/b>/p>
		p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" align="left">
		font face="Verdana" size="6">committed to bringing numerical methods to 
		undergraduates/font>/p>
		p align="left">b>font face="Verdana" size="6">Multiple Choice Test/font>/b>/p>
	/font>
  		font face="Verdana" size="6" Language="VbScript">
		p align="left">b>Euler's Method/b>/p>
		/font>
	p>&nbsp;/div>
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		font size="7" face="Georgia">b>Q1./b> To solve the ordinary differential 
		equation /font>/p>
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		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">&nbsp;/p>
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		font size="7" face="Georgia">by Euler’s method, you need to rewrite the 
		equation as/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">&nbsp;/p>
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		font size="7" face="Georgia">b>Q2/b>. Given /font>/p>
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		font face="Georgia">font size="7">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/font>span style="position: relative; top: 12.0pt">font size="7">!--[if gte vml 1]>v:shape
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		/font>/font>/p>
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		font size="7" face="Georgia"> 
		and using a step size ofi> h/i>=0.3, 
		the value ofi> y/i>(0.9)&nbsp;using 
		Euler’s method is most nearly /font>/p>
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		-36.458/font>/p>
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		font size="7" face="Georgia">
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		font size="7" face="Georgia">b>Q3/b>. Given /font>/p>
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		font face="Georgia">font size="7">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /font>
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		font size="7" face="Georgia">and using a step size of i>h/i>=0.3/font>!--[if gte mso 9]>![endif]-->font size="7" face="Georgia">, 
		the best estimate of i>dy/dx/i>(0.9)/font>!--[if gte mso 9]>![endif]-->font size="7" face="Georgia">&nbsp;using 
		Euler’s method is most nearly is/font>/p>
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		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q3" value="V1" Language="VbScript">-0.37319br>
		/font>font size="7" face="Georgia">
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		/font>font size="7" face="Georgia">
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		/font>font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q3" value="V1" Language="VbScript">-0.34341/font>/p>
		center>center>center>center>center>center>hr align="left">/center>
		/center>/center>/center>/center>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="7" face="Georgia">b>Q4/b>. The velocity (m/s) of a body is given 
		as a function of time (seconds) by/font>/p>
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		&nbsp;/p>
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		font face="Georgia" size="6">i>v/i>(i>t/i>)=200 ln(1+i>t/i>) -i>t/i>,i> 
		t&#8805;0/i>/font>i>font size="6" face="Georgia"> /font>/i>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		&nbsp;/p>
		center>
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		center>
		center>
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		font size="7" face="Georgia">Using Euler’s method with a step 
		size of 5 seconds, the distance in meters traveled by the body fromi> t/i>=2/font>!--[if gte mso 9]>![endif]-->font size="7" face="Georgia">&nbsp;to
		i>t/i>=12&nbsp;seconds 
		is most nearly /font>/p>center>
		center>
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		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q4" value="V1" Language="VbScript">3133.1 
		/font>p align="left" style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%">
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		input type="radio" style="width: 60; height: 60" name="Q4" value="V1" Language="VbScript">3939.7/font>p align="left" style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%">
		font size="7" face="Georgia"> !--[if gte mso 9]>xml>
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		input type="radio" style="width: 60; height: 60" name="Q4" value="V1" Language="VbScript">5638.0/font>p align="left" style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%">
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		center>center>center>center>center>center>center>
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		font face="Georgia">font size="7">b>Q5/b>. Euler’s method can be derived 
		by using the first two terms of the Taylor series of writing the value of
		/font>/font>!--[if gte mso 9]>![endif]-->
		font face="Georgia" size="7">i>ysub>i+1/sub>/i>/font>font face="Georgia">font size="7">i>,/i> 
		that is the value of /font>/font>font face="Georgia" size="7">i>y/i>/font>font face="Georgia">font size="7"> /font>/font>!--[if gte mso 9]>
		![endif]-->font face="Georgia">font size="7">at
		/font>/font>i>font face="Georgia" size="7">x/font>/i>font face="Georgia" size="7">i>sub>i+1/sub>/i>/font>!--[if gte mso 9]>![endif]-->font face="Georgia">font size="7">, 
		&nbsp;in terms of /font>/font>font face="Georgia" size="7">i>ysub>i/sub>/i>/font>!--[if gte mso 9]>![endif]-->font face="Georgia">font size="7">&nbsp;and 
		all the derivatives of /font>
		/font>font face="Georgia" size="7">i>ysub> /sub>/i>/font>!--[if gte mso 9]>
		![endif]-->font face="Georgia">font size="7">at
		/font>/font>i>font face="Georgia" size="7">x/font>/i>font face="Georgia" size="7">i>sub>i/sub>/i>/font>!--[if gte mso 9]>![endif]-->font face="Georgia">font size="7">.&nbsp; 
		If i>h=/i>/font>/font>i>font face="Georgia" size="7">x/font>/i>font face="Georgia" size="7">i>sub>i+1/sub>-/i>/font>i>font face="Georgia" size="7">x/font>/i>font face="Georgia" size="7">i>sub>i/sub>/i>/font>!--[if gte mso 9]>![endif]-->font face="Georgia">font size="7"> /font>/font>!--[if gte mso 9]>
		![endif]-->font face="Georgia">font size="7">, 
		the explicit expression for /font>/font>font face="Georgia" size="7">
		i>ysub>i+1/sub>/i>/font>!--[if gte mso 9]>![endif]-->font size="7" face="Georgia"> if 
		the first three terms of the Taylor series are chosen for the ordinary 
		differential equation /font>/p>
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		font face="Georgia">font size="7">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /font>
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		font size="7" face="Georgia">would be/font>/p>
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src="eulers_method_mobile_files/image020.gif" v:shapes="_x0000_s1028">![endif]>/font>/span>p align="left" style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%">
		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q5" value="V1" Language="VbScript">/font>span style="position: relative; top: 14.0pt">font size="7" face="Georgia">!--[if gte vml 1]>v:shape
 id="_x0000_s1027" type="#_x0000_t75" style='width:387pt;height:59.25pt'>
 v:imagedata src="eulers_method_mobile_files/image021.wmz" o:title=""/>
/v:shape>![endif]-->![if !vml]>img border=0 width=516 height=79
src="eulers_method_mobile_files/image022.gif" v:shapes="_x0000_s1027">![endif]>/font>/span>p align="left" style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%">
		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q5" value="V1" Language="VbScript">/font>span style="position: relative; top: 12.0pt">font size="7" face="Georgia">!--[if gte vml 1]>v:shape
 id="_x0000_s1026" type="#_x0000_t75" style='width:315.75pt;height:64.5pt'>
 v:imagedata src="eulers_method_mobile_files/image023.wmz" o:title=""/>
/v:shape>![endif]-->![if !vml]>img border=0 width=421 height=86
src="eulers_method_mobile_files/image024.gif" v:shapes="_x0000_s1026">![endif]>/font>/span>hr align="left">
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="7" face="Georgia">b>Q6./b> A homicide victim is found at 6:00PM in 
		an office building that is maintained at 72&#730;F.&nbsp; When the victim was 
		found, his body temperature was at 85 &#730;F.&nbsp; Three hours later at 9:00PM, 
		his body temperature was recorded at 78&#730;F. &nbsp;Assume the temperature of 
		the body at the time of death is the normal human body temperature of 
		98.6&#730;F.&nbsp; /font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="7" face="Georgia">The governing equation for the temperature i>&#952;/i> of the body is/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font face="Georgia">font size="7">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /font>
		span style="position: relative; top: 12.0pt">font size="7">!--[if gte vml 1]>v:shape
 id="_x0000_s1025" type="#_x0000_t75" style='width:162pt;height:59.25pt'>
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/v:shape>![endif]-->![if !vml]>img border=0 width=216 height=79
src="eulers_method_mobile_files/image026.gif" v:shapes="_x0000_s1025">![endif]>/font>/span>/font>!--[if gte mso 9]>![endif]-->/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="7" face="Georgia">where/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font face="Georgia">font size="7">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/font>/font>i>font size="6" face="Georgia">&#952;/font>/i>!--[if gte mso 9]>![endif]-->font size="6" face="Georgia">= 
		temperature of the body, &#730;F/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="6" face="Georgia">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; i>&#952;sub>a/sub>/i> = ambient 
		temperature, &#730;F/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="6" face="Georgia">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; i>t/i> = time, hours/font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="6" face="Georgia">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; i>k/i> = constant based on 
		thermal properties of the body and air./font>/p>
		p class="MsoNormal" align="left" style=" margin-top: 0; margin-bottom: 0">
		font size="7" face="Georgia">The estimated time of death most nearly is/font>/p>
		p style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%" align="left">
		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q6" value="V1" Language="VbScript">2:11 
		PM/font>font size="7">br>
		/font>
		p style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%" align="left">
		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q6" value="V1" Language="VbScript">3:13 
		PMbr>
		/font>font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q6" value="V1" Language="VbScript">4:34 
		PM/font>!--[if gte mso 9]>![endif]-->/p>
		p style="word-spacing: 0; text-indent: 0; margin: 0; line-height:120%" align="left">
		font size="7" face="Georgia">
		input type="radio" style="width: 60; height: 60" name="Q6" value="V1" Language="VbScript">5:12 
		PM/font>/p>
		p style="word-spacing: 0; text-indent: 0; margin: 0" align="left">
		!--[if gte mso 9]>![endif]-->/p>
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