007B Sample Midterm 3 - Revision history

MathAdmin: Created page with "'''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
2017-11-12T00:59:39Z

Created page with "'''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 cla..."

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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.'''

'''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]]'''