022 Exam 2 Sample B - Revision history

MathAdmin: /* Problem 5 */

2016-11-15T00:13:53Z

Problem 5

MathAdmin: /* Problem 4 */

2016-11-09T06:59:14Z

Problem 4

MathAdmin at 18:39, 28 July 2015

2015-07-28T18:39:21Z

MathAdmin: /* Problem 9 */

2015-05-17T19:25:30Z

Problem 9

MathAdmin: /* Problem 5 */

2015-05-16T00:53:51Z

Problem 5

MathAdmin: /* Problem 3 */

2015-05-16T00:22:35Z

Problem 3

MathAdmin at 23:43, 15 May 2015

2015-05-15T23:43:01Z

MathAdmin: Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the
2015-05-15T23:41:14Z

Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the <span class=..."

New page
'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. 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>

== [[022_Exam_2_Sample_A,_Problem_1| Problem 1 ]] ==
Find the derivative of  <math style="vertical-align: -60%">y\,=\,\ln \frac{(x+1)^4}{(2x - 5)(x + 4)}.</math>

== [[022_Exam_2_Sample_A,_Problem_2| Problem 2 ]] ==
 Sketch the graph of <math style="vertical-align: -52%">y = \left(\frac{1}{2}\right)^{x + 1} - 4</math>.

== [[022_Exam_2_Sample_A,_Problem_3| Problem 3 ]] ==
 Find the derivative: <math style="vertical-align: -18%">f(x) \,=\, 2x^3e^{3x+5}</math>.

== [[022_Exam_2_Sample_A,_Problem_4| Problem 4 ]] ==
 '''Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!'''

What is the present value of $3000, paid 8 years from now, in an investment that pays 6%interest,

::(a) compounded quarterly?
::(b) compounded continuously?

== [[022_Exam_2_Sample_A,_Problem_5| Problem 5 ]] ==
 Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1} dx.</math>

== [[022_Exam_2_Sample_A,_Problem_6| Problem 6 ]] ==
Find the area under the curve of  <math style="vertical-align: -13%">y = 6x^2 + 2x</math> between the <math style="vertical-align: -15%">y</math>-axis and <math style="vertical-align: -1%">x = 2</math>.

== [[022_Exam_2_Sample_A,_Problem_7| Problem 7 ]] ==
Find the antiderivatives:

::(a) <math> \int xe^{3x^2+1}\,dx.</math>
 
::(b) <math>\int_2^54x - 5\,dx.</math>

== [[022_Exam_2_Sample_A,_Problem_8| Problem 8 ]] ==

Find the quantity that produces maximum profit, given demand function <math style="vertical-align: -15%">p = 70 - 3x</math> and cost function  <math style="vertical-align: -8%">C = 120 - 30x + 2x^2.</math>

== [[022_Exam_2_Sample_A,_Problem_9| Problem 9 ]] ==

Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the min and which is the max (i.e., which test did you use?).

== [[022_Exam_2_Sample_A,_Problem_10| Problem 10 ]] ==
'''Use calculus to set up and solve the word problem:'''
A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4th side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).

@@ Line 20: / Line 20: @@
 == [[022_Exam_2_Sample_B,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1}\, dx.</math>
+<span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^{2x} + 1}\, dx.</math>
 == [[022_Exam_2_Sample_B,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==

@@ Line 14: / Line 14: @@
 <span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!'''
-<span class="exam">What is the present value of $3000, paid 8 years from now, in an investment that pays 6%interest,
+<span class="exam">What is the present value of $3000, paid 8 years from now, in an investment that pays 6% interest,
 ::<span class="exam">(a) compounded quarterly?

← Older revision		Revision as of 18:39, 28 July 2015
Line 43:		Line 43:
	<span class="exam">'''Use calculus to set up and solve the word problem:'''		<span class="exam">'''Use calculus to set up and solve the word problem:'''
	A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).		A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).
		+
		+
		+	'''Contributions to this page were made by [[Contributors\|John Simanyi]]'''

@@ Line 38: / Line 38: @@
 == [[022_Exam_2_Sample_B,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
 <span class="exam">
-Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the min and which is the max (i.e., which test did you use?).
+Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the local minimum and which is the local maximum (i.e., which test did you use?).
 == [[022_Exam_2_Sample_B,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==
 <span class="exam">'''Use calculus to set up and solve the word problem:'''
 A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).

@@ Line 20: / Line 20: @@
 == [[022_Exam_2_Sample_B,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1} dx.</math>
+<span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1}\, dx.</math>
 == [[022_Exam_2_Sample_B,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==

@@ Line 9: / Line 9: @@
 == [[022_Exam_2_Sample_B,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam"> Find the derivative: <math style="vertical-align: -18%">f(x) \,=\, 2x^3e^{3x+5}</math>.
+<span class="exam"> Find the derivative of <math style="vertical-align: -18%">f(x) \,=\, 2x^3e^{3x+5}</math>.
 == [[022_Exam_2_Sample_B,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==

@@ Line 2: / Line 2: @@
 <div class="noautonum">__TOC__</div>
-== [[022_Exam_2_Sample_A,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==
 <span class="exam">Find the derivative of &thinsp;<math style="vertical-align: -60%">y\,=\,\ln \frac{(x+1)^4}{(2x - 5)(x + 4)}.</math>
-== [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
 <span class="exam"> Sketch the graph of <math style="vertical-align: -52%">y = \left(\frac{1}{2}\right)^{x + 1} - 4</math>.
-== [[022_Exam_2_Sample_A,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
 <span class="exam"> Find the derivative: <math style="vertical-align: -18%">f(x) \,=\, 2x^3e^{3x+5}</math>.
-== [[022_Exam_2_Sample_A,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
 <span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers-not solve for the particular values!'''
@@ Line 19: / Line 19: @@
 ::<span class="exam">(b) compounded continuously?
-== [[022_Exam_2_Sample_A,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
 <span class="exam"> Find the antiderivative of <math>\int \frac{2e^{2x}}{e^2x + 1} dx.</math>
-== [[022_Exam_2_Sample_A,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==
 <span class="exam">Find the area under the curve of&thinsp; <math style="vertical-align: -13%">y = 6x^2 + 2x</math> between the <math style="vertical-align: -15%">y</math>-axis and <math style="vertical-align: -1%">x = 2</math>.
-== [[022_Exam_2_Sample_A,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==
 <span class="exam">Find the antiderivatives:
@@ Line 32: / Line 32: @@
 ::<span class="exam">(b) <math>\int_2^54x - 5\,dx.</math>
-== [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==
 <span class="exam">
 Find the quantity that produces maximum profit, given demand function <math style="vertical-align: -15%">p = 70 - 3x</math> and cost function&thinsp; <math style="vertical-align: -8%">C = 120 - 30x + 2x^2.</math>
-== [[022_Exam_2_Sample_A,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
 <span class="exam">
 Find all relative extrema and points of inflection for the function <math style="vertical-align: -16%">g(x) = x^3 - 3x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph. Explain how you know which point is the min and which is the max (i.e., which test did you use?).
-== [[022_Exam_2_Sample_A,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==
+== [[022_Exam_2_Sample_B,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==
 <span class="exam">'''Use calculus to set up and solve the word problem:'''
 A fence is to be built to enclose a rectangular region of 480 square feet. The fencing material along three sides cost $2 per foot. The fencing material along the 4<sup>th</sup> side costs $6 per foot. Find the most economical dimensions of the region (that is, minimize the cost).