009B Sample Midterm 1 - Revision history

MathAdmin: /* Problem 3 */

2017-11-20T18:04:12Z

Problem 3

MathAdmin: /* Problem 5 */

2017-11-12T23:07:42Z

Problem 5

MathAdmin: /* Problem 5 */

2017-11-12T23:07:28Z

Problem 5

MathAdmin: /* Problem 4 */

2017-11-12T23:04:55Z

Problem 4

MathAdmin: /* Problem 2 */

2017-11-12T23:02:27Z

Problem 2

MathAdmin: /* Problem 1 */

2017-11-12T22:46:41Z

Problem 1

MathAdmin at 18:58, 9 April 2017

2017-04-09T18:58:58Z

MathAdmin at 20:35, 18 April 2016

2016-04-18T20:35:17Z

MathAdmin: /* Problem 5 */

2016-02-06T21:18:05Z

Problem 5

MathAdmin: Created page with "'''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''' '''
2016-02-01T22:34:19Z

Created page with "'''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 clas..."

New page
'''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''' ''' boxed problem numbers  to go to a solution.'''
<div class="noautonum">TOC</div>

== [[009B_Sample Midterm 1,_Problem_1| Problem 1 ]] ==
Evaluate the indefinite and definite integrals.

::a) <math>\int x^2\sqrt{1+x^3}~dx</math>
::b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math>

== [[009B_Sample Midterm 1,_Problem_2| Problem 2 ]] ==
 Find the average value of the function on the given interval.

::<math>f(x)=2x^3(1+x^2)^4,~~~[0,2]</math>

== [[009B_Sample Midterm 1,_Problem_3| Problem 3 ]] ==
 Evaluate the indefinite and definite integrals.

::a) <math>\int x^2 e^x~dx</math>
::b) <math>\int_{1}^{e} x^3\ln x~dx</math>

== [[009B_Sample Midterm 1,_Problem_4| Problem 4 ]] ==
 Evaluate the integral:

::<math>\int \sin^3x \cos^2x~dx</math>

== [[009B_Sample Midterm 1,_Problem_5| Problem 5 ]] ==
 Let <math style="vertical-align: -5px">f(x)=1-x^2</math>.

::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.
::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.
::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.

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 == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam"> Evaluate the indefinite and definite integrals.
+<span class="exam"> A population grows at a rate
-<span class="exam">(a) &nbsp; <math>\int x^2 e^x~dx</math>
+::<math>P'(t)=500e^{-t}</math>
-<span class="exam">(b) &nbsp; <math>\int_{1}^{e} x^3\ln x~dx</math>
+<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.
 == [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==

← Older revision		Revision as of 23:07, 12 November 2017
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	::<math>\int \sin^3x \cos^2x~dx</math>		::<math>\int \sin^3x \cos^2x~dx</math>
		+
		+
		+

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

@@ Line 35: / Line 35: @@
 == [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Let &nbsp;<math style="vertical-align: -5px">f(x)=1-x^2</math>.
+<span class="exam"> Evaluate the integral:
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

@@ Line 28: / Line 28: @@
 == [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
-<span class="exam"> Evaluate the integral:
+<span class="exam"> Evaluate the indefinite and definite integrals.
-::<math>\int \sin^3x \cos^2x~dx</math>
+<span class="exam">(a) &nbsp; <math>\int x^2 e^x~dx</math>
 == [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

@@ Line 14: / Line 14: @@
 == [[009B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-<span class="exam"> Otis Taylor plots the price per share of a stock that he owns as a function of time
+<span class="exam">Evaluate the indefinite and definite integrals.
-<span class="exam">and finds that it can be approximated by the function
+<span class="exam">(a) &nbsp; <math>\int x^2\sqrt{1+x^3}~dx</math>
-::<math>s(t)=t(25-5t)+18</math>
+<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_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==

@@ Line 1: / Line 1: @@
 '''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;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
@@ Line 7: / Line 7: @@
 <span class="exam">Evaluate the indefinite and definite integrals.
-::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}~dx</math>
+<span class="exam">(a) &nbsp; <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_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-<span class="exam"> Find the average value of the function on the given interval.
+<span class="exam"> Otis Taylor plots the price per share of a stock that he owns as a function of time
-::<math>f(x)=2x^3(1+x^2)^4,~~~[0,2]</math>
+<span class="exam">where &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; is the time (in years) since the stock was purchased.
 == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
 <span class="exam"> Evaluate the indefinite and definite integrals.
-::<span class="exam">a) <math>\int x^2 e^x~dx</math>
+<span class="exam">(a) &nbsp; <math>\int x^2 e^x~dx</math>
-::<span class="exam">b) <math>\int_{1}^{e} x^3\ln x~dx</math>
 == [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
@@ Line 28: / Line 35: @@
 == [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Let <math style="vertical-align: -5px">f(x)=1-x^2</math>.
+<span class="exam"> Let &nbsp;<math style="vertical-align: -5px">f(x)=1-x^2</math>.
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

← Older revision		Revision as of 20:35, 18 April 2016
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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. Click on the''' '''<span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''	+	'''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>		<div class="noautonum">__TOC__</div>

← Older revision		Revision as of 21:18, 6 February 2016
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	::<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">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.		::<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.
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''