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'''This is a sample, and is meant to represent the material usually covered in Math 7B for the midterm. An actual test may or may not be similar.'''

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'''Click on the <span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''

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<div class="noautonum">__TOC__</div>

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== [[007B_Sample Midterm 3,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==

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<span class="exam"> Divide the interval &nbsp;<math style="vertical-align: -5px">[0,\pi]</math>&nbsp; into four subintervals of equal length &nbsp; <math>\frac{\pi}{4}</math>&nbsp; and compute the right-endpoint Riemann sum of &nbsp;<math style="vertical-align: -5px">y=\sin (x).</math>

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== [[007B_Sample Midterm 3,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==

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<span class="exam"> Compute the following integrals:

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<span class="exam">(a) &nbsp; <math>\int x^2\sin (x^3) ~dx</math> 

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<span class="exam">(b) &nbsp; <math>\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \cos^2(x)\sin (x)~dx</math>

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== [[007B_Sample Midterm 3,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==

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<span class="exam"> For a fish that starts life with a length of 1cm and has a maximum length of 30cm, the von Bertalanffy growth model predicts that the growth rate is &nbsp;<math style="vertical-align: 0px">29e^{-t}</math>&nbsp; cm/year where &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; is the age of the fish. What is the average length of the fish over its first five years?

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== [[007B_Sample Midterm 3,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==

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<span class="exam"> Find the volume of the solid obtained by rotating the region bounded by &nbsp;<math style="vertical-align: -5px">y=\sqrt{\sin x},~0\le x\le \pi,</math>&nbsp; and &nbsp;<math>y=0</math>&nbsp; about the &nbsp;<math style="vertical-align: 0px">x-</math>axis. Sketch the graph of the region and a typical disk element.

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== [[007B_Sample Midterm 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

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<span class="exam"> Evaluate the following integrals.

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<span class="exam">(a) &nbsp; <math>\int x\sin x ~dx</math> 

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<span class="exam">(b) &nbsp; <math>\int \frac{1}{(x-3)(x-2)}~dx</math>

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'''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

← Older revision		Revision as of 23:09, 2 November 2017
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−	~~text~~	+	'''This is a sample, and is meant to represent the material usually covered in Math 7B for the midterm. An actual test may or may not be similar.'''
		+
		+	'''Click on the <span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''
		+	<div class="noautonum">__TOC__</div>
		+
		+	== [[007B_Sample Midterm 3,_Problem_1\|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==
		+	<span class="exam"> Divide the interval  <math style="vertical-align: -5px">[0,\pi]</math>  into four subintervals of equal length   <math>\frac{\pi}{4}</math>  and compute the right-endpoint Riemann sum of  <math style="vertical-align: -5px">y=\sin (x).</math>
		+
		+	== [[007B_Sample Midterm 3,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==
		+	<span class="exam"> Compute the following integrals:
		+
		+	<span class="exam">(a)   <math>\int x^2\sin (x^3) ~dx</math>
		+
		+	<span class="exam">(b)   <math>\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \cos^2(x)\sin (x)~dx</math>
		+
		+	== [[007B_Sample Midterm 3,_Problem_3\|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] ==
		+	<span class="exam"> For a fish that starts life with a length of 1cm and has a maximum length of 30cm, the von Bertalanffy growth model predicts that the growth rate is  <math style="vertical-align: 0px">29e^{-t}</math>  cm/year where  <math style="vertical-align: 0px">t</math>  is the age of the fish. What is the average length of the fish over its first five years?
		+
		+
		+	== [[007B_Sample Midterm 3,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==
		+	<span class="exam"> Find the volume of the solid obtained by rotating the region bounded by  <math style="vertical-align: -5px">y=\sqrt{\sin x},~0\le x\le \pi,</math>  and  <math>y=0</math>  about the  <math style="vertical-align: 0px">x-</math>axis. Sketch the graph of the region and a typical disk element.
		+
		+
		+	== [[007B_Sample Midterm 3,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
		+	<span class="exam"> Evaluate the following integrals.
		+
		+	<span class="exam">(a)   <math>\int x\sin x ~dx</math>
		+
		+	<span class="exam">(b)   <math>\int \frac{1}{(x-3)(x-2)}~dx</math>
		+
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''

007B Sample Midterm 3 - Revision history

Kayla Murray at 23:09, 2 November 2017

Kayla Murray: Created page with "text"