009B Sample Final 1 - Revision history

MathAdmin at 16:40, 10 April 2017

2017-04-10T16:40:00Z

2016-04-18T20:25:14Z

Problem 7

2016-04-18T20:19:10Z

2016-04-18T19:43:28Z

Problem 2

2016-04-18T19:43:01Z

Problem 2

2016-04-18T19:36:53Z

Problem 1

2016-04-18T19:35:59Z

Problem 7

2016-04-18T19:35:35Z

Problem 7

2016-04-18T19:35:12Z

Problem 6

2016-04-18T19:34:56Z

Problem 5

@@ Line 73: / Line 73: @@
 ::::::<math>y=1-x^2,~~~0\leq x \leq 1</math>
-::<span class="exam">is rotated about the <math style="vertical-align: -3px">y</math>-axis. Find the area of the resulting surface.
+:::<span class="exam">is rotated about the <math style="vertical-align: -3px">y</math>-axis. Find the area of the resulting surface.
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

← Older revision		Revision as of 20:19, 18 April 2016
Line 1:		Line 1:
−	'''This is a sample, and is meant to represent the material usually covered in Math 9B for the final. 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 final. 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>

@@ Line 16: / Line 16: @@
 ::::::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg).</math>
-::<span class="exam">a) Compute <math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt</math>.
+::<span class="exam">a) Compute <math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt.</math>
 ::<span class="exam">b) Find <math style="vertical-align: -5px">f'(x).</math>

@@ Line 18: / Line 18: @@
 ::<span class="exam">a) Compute <math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt</math>.
-::<span class="exam">b) Find <math style="vertical-align: -5px">f'(x)</math>.
+::<span class="exam">b) Find <math style="vertical-align: -5px">f'(x).</math>
 ::<span class="exam">c) State the Fundamental Theorem of Calculus.

@@ Line 4: / Line 4: @@
 == [[009B_Sample Final 1,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
 <span class="exam">Consider the region bounded by the following two functions:
-::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
+::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0.</math>
 ::<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.

@@ Line 63: / Line 63: @@
 == [[009B_Sample Final 1,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==
-<span class="exam">a) Find the length of the curve
+::<span class="exam">a) Find the length of the curve
 ::::::<math>y=\ln (\cos x),~~~0\leq x \leq \frac{\pi}{3}</math>.
-<span class="exam">b) The curve
+::<span class="exam">b) The curve
 ::::::<math>y=1-x^2,~~~0\leq x \leq 1</math>

@@ Line 57: / Line 57: @@
 <span class="exam"> Evaluate the improper integrals:
-<span class="exam">a) <math>\int_0^{\infty} xe^{-x}~dx</math>
+::<span class="exam">a) <math>\int_0^{\infty} xe^{-x}~dx</math>
-<span class="exam">b) <math>\int_1^4 \frac{dx}{\sqrt{4-x}}</math>
+::<span class="exam">b) <math>\int_1^4 \frac{dx}{\sqrt{4-x}}</math>
 == [[009B_Sample Final 1,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==

@@ Line 46: / Line 46: @@
 ::::::<span class="exam"> <math style="vertical-align: 0px">x=0</math>, <math style="vertical-align: -4px">y=e^x</math>, and <math style="vertical-align: -4px">y=ex</math>.
-<span class="exam">a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:
+::<span class="exam">a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:
-:<span class="exam"><math style="vertical-align: -4px">y=e^x</math> and <math style="vertical-align: -4px">y=ex</math>. (There is only one.)
+::::::<span class="exam"><math style="vertical-align: -4px">y=e^x</math> and <math style="vertical-align: -4px">y=ex</math>. (There is only one.)
-<span class="exam">b) Set up the integral for the volume of the solid.
+::<span class="exam">b) Set up the integral for the volume of the solid.
-<span class="exam">c) Find the volume of the solid by computing the integral.
+::<span class="exam">c) Find the volume of the solid by computing the integral.
 == [[009B_Sample Final 1,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==