007B Sample Midterm 1 - Revision history

Kayla Murray at 23:01, 2 November 2017

2017-11-02T23:01:01Z

Kayla Murray at 22:49, 2 November 2017

2017-11-02T22:49:36Z

Kayla Murray: /* Problem 5 */

2017-11-02T22:48:29Z

Problem 5

Kayla Murray: /* Problem 2 */

2017-11-02T22:46:27Z

Problem 2

Kayla Murray at 22:44, 2 November 2017

2017-11-02T22:44:08Z

Kayla Murray: Created page with "text"

2017-11-02T22:33:55Z

Created page with "text"

New page

text

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 <div class="noautonum">__TOC__</div>
-== [[009B_Sample Midterm 1,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
+== [[007B_Sample Midterm 1,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
 <span class="exam"> Let &nbsp;<math style="vertical-align: -5px">f(x)=1-x^2</math>.
@@ Line 13: / Line 13: @@
 <span class="exam">(c) Express &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
-== [[009B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
+== [[007B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
 <span class="exam"> A population grows at a rate
@@ Line 24: / Line 24: @@
 <span class="exam">(b) &nbsp; Use your answer to part (a) to find the size of the population after one month.
-== [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
+== [[007B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
 <span class="exam">Evaluate the following integrals.
@@ Line 31: / Line 31: @@
 <span class="exam">(b) &nbsp; <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math>
-== [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
+== [[007B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
 <span class="exam"> Evaluate the following integrals.
@@ Line 38: / Line 38: @@
 <span class="exam">(b) &nbsp; <math>\int \frac{5x-7}{x^2-3x+2}~dx</math>
-== [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
+== [[007B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
 <span class="exam"> Find the area bounded by &nbsp;<math style="vertical-align: -5px">y=\sin(x)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">y=\cos(x)</math>&nbsp; from &nbsp;<math style="vertical-align: -1px">x=0</math>&nbsp; to &nbsp;<math style="vertical-align: -14px">x=\frac{\pi}{4}.</math>
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

← Older revision		Revision as of 22:49, 2 November 2017
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−	'''This is a sample, and is meant to represent the material usually covered in Math 9B for the midterm. An actual test may or may not be similar.'''	+	'''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.'''		'''Click on the''' '''<span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''

@@ Line 39: / Line 39: @@
 == [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Find the area bounded by &nbsp;<math>y=\sin(x)</math>&nbsp; and &nbsp;<math>y=\cos(x)</math>&nbsp; from &nbsp;<math>x=0</math>&nbsp; to &nbsp;<math>x=\frac{\pi}{4}.</math>
+<span class="exam"> Find the area bounded by &nbsp;<math style="vertical-align: -5px">y=\sin(x)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">y=\cos(x)</math>&nbsp; from &nbsp;<math style="vertical-align: -1px">x=0</math>&nbsp; to &nbsp;<math style="vertical-align: -14px">x=\frac{\pi}{4}.</math>
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

@@ Line 18: / Line 18: @@
 ::<math>P'(t)=500e^{-t}</math>
-<span class="exam">where &nbsp;<math>P(t)</math>&nbsp; is the population after &nbsp;<math>t</math>&nbsp; months.
+<span class="exam">where &nbsp;<math style="vertical-align: -5px">P(t)</math>&nbsp; is the population after &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; months.
-<span class="exam">(a) &nbsp; Find a formula for the population size after &nbsp;<math>t</math>&nbsp; months, given that the population is &nbsp;<math>2000</math>&nbsp; at &nbsp;<math>t=0.</math>
+<span class="exam">(a) &nbsp; Find a formula for the population size after &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; months, given that the population is &nbsp;<math style="vertical-align: 0px">2000</math>&nbsp; at &nbsp;<math style="vertical-align: 0px">t=0.</math>
 <span class="exam">(b) &nbsp; Use your answer to part (a) to find the size of the population after one month.
 == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==

← Older revision		Revision as of 22:44, 2 November 2017
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−	~~text~~	+	'''This is a sample, and is meant to represent the material usually covered in Math 9B 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>
		+
		+	== [[009B_Sample Midterm 1,_Problem_1\|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==
		+	<span class="exam"> Let  <math style="vertical-align: -5px">f(x)=1-x^2</math>.
		+
		+	<span class="exam">(a) Compute the left-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
		+
		+	<span class="exam">(b) Compute the right-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
		+
		+	<span class="exam">(c) Express  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
		+
		+	== [[009B_Sample Midterm 1,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==
		+	<span class="exam"> A population grows at a rate
		+
		+	::<math>P'(t)=500e^{-t}</math>
		+
		+	<span class="exam">where  <math>P(t)</math>  is the population after  <math>t</math>  months.
		+
		+	<span class="exam">(a)   Find a formula for the population size after  <math>t</math>  months, given that the population is  <math>2000</math>  at  <math>t=0.</math>
		+
		+	<span class="exam">(b)   Use your answer to part (a) to find the size of the population after one month.
		+
		+	== [[009B_Sample Midterm 1,_Problem_3\|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] ==
		+	<span class="exam">Evaluate the following integrals.
		+
		+	<span class="exam">(a)   <math>\int x^2\sqrt{1+x^3}~dx</math>
		+
		+	<span class="exam">(b)   <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math>
		+
		+	== [[009B_Sample Midterm 1,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==
		+	<span class="exam"> Evaluate the following integrals.
		+
		+	<span class="exam">(a)   <math>\int x^2 e^x~dx</math>
		+
		+	<span class="exam">(b)   <math>\int \frac{5x-7}{x^2-3x+2}~dx</math>
		+
		+	== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
		+	<span class="exam"> Find the area bounded by  <math>y=\sin(x)</math>  and  <math>y=\cos(x)</math>  from  <math>x=0</math>  to  <math>x=\frac{\pi}{4}.</math>
		+
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''