009B Sample Midterm 3 - Revision history

MathAdmin: /* Problem 5 */

2017-11-24T01:18:30Z

Problem 5

MathAdmin: /* Problem 3 */

2017-11-24T01:16:24Z

Problem 3

MathAdmin: /* Problem 4 */

2017-11-13T01:35:25Z

Problem 4

MathAdmin at 19:17, 9 April 2017

2017-04-09T19:17:54Z

MathAdmin: /* Problem 5 */

2016-05-12T22:48:28Z

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
2016-04-19T00:37:55Z

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 cla..."

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

== [[009B_Sample Midterm 3,_Problem_1| Problem 1 ]] ==
 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>

== [[009B_Sample Midterm 3,_Problem_2| Problem 2 ]] ==
 State the fundamental theorem of calculus, and use this theorem to find the derivative of

::<math>F(x)=\int_{\cos (x)}^5 \frac{1}{1+u^{10}}~du.</math>

== [[009B_Sample Midterm 3,_Problem_3| Problem 3 ]] ==
 Compute the following integrals:

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

== [[009B_Sample Midterm 3,_Problem_4| Problem 4 ]] ==
 Evaluate the integral:

::<math>\int \sin (\ln x)~dx.</math>

== [[009B_Sample Midterm 3,_Problem_5| Problem 5 ]] ==
 Evaluate the indefinite and definite integrals.

::a) <math>\int \tan^3x ~dx</math>
::b) <math>\int_0^\pi \sin^2x~dx</math>

@@ Line 29: / Line 29: @@
 <span class="exam"> Evaluate the indefinite and definite integrals.
-<span class="exam">(a) &nbsp; <math>\int \tan^3x ~dx</math>
+<span class="exam">(a) &nbsp; <math>\int x\ln x ~dx</math>
 <span class="exam">(b) &nbsp; <math>\int_0^\pi \sin^2x~dx</math>

@@ Line 13: / Line 13: @@
 == [[009B_Sample Midterm 3,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam"> Compute the following integrals:
+<span class="exam"> Find a curve &nbsp;<math style="vertical-align: -5px">y=f(x)</math>&nbsp; with the following properties:
-<span class="exam">(a) &nbsp; <math>\int x^2\sin (x^3) ~dx</math>
+<span class="exam">(i) &nbsp; <math style="vertical-align: -5px">f''(x)=6x</math>
-<span class="exam">(b) &nbsp; <math>\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \cos^2(x)\sin (x)~dx</math>
+<span class="exam">(ii) &nbsp; Its graph passes through the point &nbsp;<math style="vertical-align: -5px">(0,1)</math>&nbsp; and has a horizontal tangent there.
 == [[009B_Sample Midterm 3,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==

@@ Line 20: / Line 20: @@
 == [[009B_Sample Midterm 3,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
-<span class="exam"> The rate of reaction to a drug is given by:
+<span class="exam"> Compute the following integrals:
-::<math>r'(t)=2t^2e^{-t}</math>
+<span class="exam">(a) &nbsp; <math>\int x^2\sin (x^3) ~dx</math>
-<span class="exam">where &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; is the number of hours since the drug was administered.
+<span class="exam">(b) &nbsp; <math>\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \cos^2(x)\sin (x)~dx</math>
 == [[009B_Sample Midterm 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

@@ Line 5: / Line 5: @@
 == [[009B_Sample Midterm 3,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</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>
+<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>
 == [[009B_Sample Midterm 3,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
@@ Line 15: / Line 15: @@
 <span class="exam"> Compute the following integrals:
-::<span class="exam">a) <math>\int x^2\sin (x^3) ~dx</math>
+<span class="exam">(a) &nbsp; <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>
 == [[009B_Sample Midterm 3,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
-<span class="exam"> Evaluate the integral:
+<span class="exam"> The rate of reaction to a drug is given by:
-::<math>\int \sin (\ln x)~dx.</math>
+::<math>r'(t)=2t^2e^{-t}</math>
 == [[009B_Sample Midterm 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
 <span class="exam"> Evaluate the indefinite and definite integrals.
-::<span class="exam">a) <math>\int \tan^3x ~dx</math>
+<span class="exam">(a) &nbsp; <math>\int \tan^3x ~dx</math>
-::<span class="exam">b) <math>\int_0^\pi \sin^2x~dx</math>
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

← Older revision		Revision as of 22:48, 12 May 2016
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	::<span class="exam">a) <math>\int \tan^3x ~dx</math>		::<span class="exam">a) <math>\int \tan^3x ~dx</math>
	::<span class="exam">b) <math>\int_0^\pi \sin^2x~dx</math>		::<span class="exam">b) <math>\int_0^\pi \sin^2x~dx</math>
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''