009B Sample Midterm 2 - Revision history

MathAdmin at 19:13, 9 April 2017

2017-04-09T19:13:52Z

MathAdmin: /* Problem 1 */

2016-04-18T21:28:00Z

Problem 1

MathAdmin at 21:23, 18 April 2016

2016-04-18T21:23:39Z

MathAdmin: /* Problem 5 */

2016-02-06T21:19:54Z

Problem 5

MathAdmin: /* Problem 3 */

2016-02-03T16:17:25Z

Problem 3

MathAdmin: /* Problem 1 */

2016-02-03T16:16:21Z

Problem 1

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''' '''
2016-02-03T06:56:12Z

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 cl..."

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 2,_Problem_1| Problem 1 ]] ==
 Consider the region <math style="vertical-align: 0px">S</math> bounded by <math style="vertical-align: -13px">x=1,x=5,y=\frac{1}{x^2}</math> and the <math>x</math>-axis.

::a) Use four rectangles and a Riemann sum to approximate the area of the region <math style="vertical-align: 0px">S</math>. Sketch the region <math style="vertical-align: 0px">S</math> and the rectangles and indicate whether your rectangles overestimate or underestimate the area of <math style="vertical-align: 0px">S</math>.
::b) Find an expression for the area of the region <math style="vertical-align: 0px">S</math> as a limit. Do not evaluate the limit.

== [[009B_Sample Midterm 2,_Problem_2| Problem 2 ]] ==
 This problem has three parts:

::a) State the Fundamental Theorem of Calculus.

::b) Compute   <math style="vertical-align: -15px">\frac{d}{dx}\int_0^{\cos (x)}\sin (t)~dt</math>.

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

== [[009B_Sample Midterm 2,_Problem_3| Problem 3 ]] ==
 Evaluate

::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>

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

== [[009B_Sample Midterm 2,_Problem_4| Problem 4 ]] ==
 Evaluate the integral:

::<math>\int e^{-2x}\sin (2x)~dx</math>

== [[009B_Sample Midterm 2,_Problem_5| Problem 5 ]] ==
 Evaluate the integral:

::<math>\int \tan^4 x ~dx</math>

@@ 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.'''
+'''Click on the <span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
 <div class="noautonum">__TOC__</div>
 == [[009B_Sample Midterm 2,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
-<span class="exam"> Consider the region <math style="vertical-align: 0px">S</math> bounded by <math style="vertical-align: -13px">x=1,x=5,y=\frac{1}{x^2}</math>&thinsp; and the <math>x</math>-axis.
+<span class="exam"> This problem has three parts:
-::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math style="vertical-align: 0px">S</math>. Sketch the region <math style="vertical-align: 0px">S</math> and the rectangles and
+<span class="exam">(a) State the Fundamental Theorem of Calculus.
-:::<span class="exam">indicate whether your rectangles overestimate or underestimate the area of <math style="vertical-align: 0px">S</math>.
+<span class="exam">(b) Compute &nbsp; <math style="vertical-align: -15px">\frac{d}{dx}\int_0^{\cos (x)}\sin (t)~dt</math>.
-::<span class="exam">b) Find an expression for the area of the region <math style="vertical-align: 0px">S</math> as a limit. Do not evaluate the limit.
 == [[009B_Sample Midterm 2,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-<span class="exam"> This problem has three parts:
+<span class="exam"> Evaluate
-::<span class="exam">a) State the Fundamental Theorem of Calculus.
+<span class="exam">(a) &nbsp; <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) Compute &thinsp; <math style="vertical-align: -15px">\frac{d}{dx}\int_0^{\cos (x)}\sin (t)~dt</math>.
+<span class="exam">(b) &nbsp; <math style="vertical-align: -14px">\int_0^2 (x^3+x)\sqrt{x^4+2x^2+4}~dx</math>
-::<span class="exam">c) Evaluate <math style="vertical-align: -14px">\int_{0}^{\pi/4}\sec^2 x~dx</math>.
+== [[009B_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-== [[009B_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
+::<math>v(t)=-32t+200</math>
-::<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">feet per second. Determine the total distance traveled by the particle
-::<span class="exam">b) <math style="vertical-align: -14px">\int_0^2 (x^3+x)\sqrt{x^4+2x^2+4}~dx</math>
+<span class="exam">from time &nbsp;<math style="vertical-align: 0px">t=0</math>&nbsp; to time &nbsp;<math style="vertical-align: -1px">t=10.</math>
 == [[009B_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
@@ Line 37: / Line 38: @@
 ::<math>\int \tan^4 x ~dx</math>
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

@@ Line 7: / Line 7: @@
 <span class="exam"> Consider the region <math style="vertical-align: 0px">S</math> bounded by <math style="vertical-align: -13px">x=1,x=5,y=\frac{1}{x^2}</math>&thinsp; and the <math>x</math>-axis.
-::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math style="vertical-align: 0px">S</math>. Sketch the region <math style="vertical-align: 0px">S</math> and the rectangles and indicate whether your rectangles overestimate or underestimate the area of <math style="vertical-align: 0px">S</math>.
+::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math style="vertical-align: 0px">S</math>. Sketch the region <math style="vertical-align: 0px">S</math> and the rectangles and
 ::<span class="exam">b) Find an expression for the area of the region <math style="vertical-align: 0px">S</math> as a limit. Do not evaluate the limit.

@@ 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'''
+'''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.'''
-'''<span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
+'''Click on the '''<span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> '''to go to a solution.'''
 <div class="noautonum">__TOC__</div>

← Older revision		Revision as of 21:19, 6 February 2016
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	::<math>\int \tan^4 x ~dx</math>		::<math>\int \tan^4 x ~dx</math>
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''

@@ Line 20: / Line 20: @@
 == [[009B_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam"> Evaluate
+<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>