007B Sample Midterm 2 - 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
2017-11-12T00:58:43Z

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 cl..."

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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.'''
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== [[007B_Sample Midterm 2,_Problem_1|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==
<span class="exam"> This problem has three parts:

<span class="exam">(a) State both parts of the fundamental theorem of calculus.

<span class="exam">(b) Compute   <math style="vertical-align: -15px">\frac{d}{dx}\int_2^{\cos (x)}\sin (t)~dt</math>.

<span class="exam">(c) Evaluate  <math style="vertical-align: -14px">\int_{0}^{\pi/4}\sec^2 x~dx</math>.

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

<span class="exam">(a)   <math style="vertical-align: -14px">\int_1^2\bigg(2t+\frac{3}{t^2}\bigg)\bigg(4t^2-\frac{5}{t}\bigg)~dt</math>

<span class="exam">(b)   <math style="vertical-align: -14px">\int_0^2 (x^3+x)\sqrt{x^4+2x^2+4}~dx</math>

== [[007B_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] ==
<span class="exam">The population density of a plant species is  <math style="vertical-align: -5px">f(x)</math>  individual per square meter, where  <math style="vertical-align: 0px">x</math>  is the distance from the river, with  <math style="vertical-align: -5px">f(x)\ge 0</math>  for  <math style="vertical-align: -3px">x\le 100</math>  and  <math style="vertical-align: -5px">f(x)=0</math>  for  <math style="vertical-align: -3px">x\ge 100.</math> Construct a definite integral to calculate the number of plants along a section of the river of length  <math style="vertical-align: 0px">L.</math>

== [[007B_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==
<span class="exam"> Find the area of the region bounded by  <math style="vertical-align: -4px">y=\ln x,~y=0,~x=1,</math>  and  <math style="vertical-align: 0px">x=e.</math>

== [[007B_Sample Midterm 2,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
<span class="exam"> Evaluate the integral:

::<math>\int \frac{4x}{(x+1)(x^2+1)} ~dx</math>

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