022 Exam 1 Sample A - Revision history

MathAdmin at 18:40, 28 July 2015

2015-07-28T18:40:06Z

MathAdmin: /* Marginal Revenue and Profit */

2015-04-14T02:31:17Z

Marginal Revenue and Profit

MathAdmin: /* Marginal Revenue and Profit */

2015-04-14T02:30:53Z

Marginal Revenue and Profit

MathAdmin: /* Marginal Revenue and Profit */

2015-04-14T02:08:43Z

Marginal Revenue and Profit

MathAdmin: /* Related Rates (Word Problem) */

2015-04-13T05:43:39Z

Related Rates (Word Problem)

MathAdmin: /* Definition of the Derivative */

2015-04-12T18:23:00Z

Definition of the Derivative

MathAdmin at 18:22, 12 April 2015

2015-04-12T18:22:42Z

MathAdmin at 18:19, 12 April 2015

2015-04-12T18:19:10Z

MathAdmin at 17:27, 12 April 2015

2015-04-12T17:27:20Z

MathAdmin: /* Continuity and Limits */

2015-04-12T05:30:23Z

Continuity and Limits

← Older revision		Revision as of 18:40, 28 July 2015
Line 59:		Line 59:
	fixed cost is $400, the variable cost formula is <math style="vertical-align: -5%">x^{2}+30x</math>,		fixed cost is $400, the variable cost formula is <math style="vertical-align: -5%">x^{2}+30x</math>,
	and the current production quantity is 9 units.		and the current production quantity is 9 units.
		+
		+
		+	'''Contributions to this page were made by [[Contributors\|John Simanyi]]'''

@@ Line 28: / Line 28: @@
 <span class="exam">[[022_Exam_1_Sample_A,_Problem_5 |<span class="biglink">&nbsp;Problem 5.&nbsp;</span>]] Find the marginal revenue and marginal profit at <math style="vertical-align: -3%">x=4</math>, given the demand function
-<math>p=\frac{200}{\sqrt{x}}</math>
+::<math>p=\frac{200}{\sqrt{x}}</math>
 <span class="exam">and the cost function
-<math>C(x)=100+15x+3x^{2}.</math>
+::<math>C(x)=100+15x+3x^{2}.</math>
 <span class="exam">Should the firm produce one more item under these conditions? Justify

@@ Line 32: / Line 32: @@
 <span class="exam">and the cost function
-<math>C=100+15x+3x^{2}.</math>
+<math>C(x)=100+15x+3x^{2}.</math>
 <span class="exam">Should the firm produce one more item under these conditions? Justify

@@ Line 30: / Line 30: @@
 <math>p=\frac{200}{\sqrt{x}}</math>
-<span style="font-size:135%">and the cost function
+<span class="exam">and the cost function
 <math>C=100+15x+3x^{2}.</math>

@@ Line 42: / Line 42: @@
 the ladder is pulled away from the house at a rate of 2 feet per second.
 How fast is the top of the ladder moving down the wall when the base
-of the ladder is 9 feet from the house.
+of the ladder is 9 feet from the house?
 == Slope of Tangent Line ==

@@ Line 3: / Line 3: @@
 == Definition of the Derivative ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_1|<span class="biglink">&nbsp;Problem 1.&nbsp;</span>']] Use the definition of derivative to find the derivative
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_1|<span class="biglink">&nbsp;Problem 1.&nbsp;</span>]] Use the definition of derivative to find the derivative
 of <math style="vertical-align: -15%">f(x)=\sqrt{x-5}</math>.

@@ Line 1: / Line 1: @@
-'''This is a sample, and is meant to represent the material usually covered in Math 22 up to the first exam. An actual test may or may not be similar. Click on the <span style="color:blue;">blue problem numbers</span> to go to a solution.'''
+'''This is a sample, and is meant to represent the material usually covered in Math 22 up to the first exam. 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.'''
 == Definition of the Derivative ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_1|'''Problem 1.''']] Use the definition of derivative to find the derivative
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_1|<span class="biglink">&nbsp;Problem 1.&nbsp;</span>']] Use the definition of derivative to find the derivative
 of <math style="vertical-align: -15%">f(x)=\sqrt{x-5}</math>.
 == Implicit Differentiation ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_2 |'''Problem 2.''']] Use implicit differentiation to find <math style="vertical-align: -16%;">dy/dx</math> at the
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_2 |<span class="biglink">&nbsp;Problem 2.&nbsp;</span>]] Use implicit differentiation to find <math style="vertical-align: -16%;">dy/dx</math> at the
 point <math style="vertical-align: -17%;">(1,0)</math> on the curve defined by <math style="vertical-align: -12%;">x^{3}-y^{3}-y=x</math>.
 == Continuity and Limits ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_3 |'''Problem 3.''']] Given a function <math style="vertical-align: -40%;">g(x)=\frac{x+5}{x^{2}-25}</math>&thinsp;,
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_3 |<span class="biglink">&nbsp;Problem 3.&nbsp;</span>]] Given a function <math style="vertical-align: -40%;">g(x)=\frac{x+5}{x^{2}-25}</math>&thinsp;,
 :<span class="exam">(a) Find the intervals where <math style="vertical-align: -20%;">g(x)</math> is continuous.
@@ Line 21: / Line 21: @@
 == Increasing and Decreasing ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_4 |'''Problem 4.''']] Determine the intervals where the function&thinsp; <math style="vertical-align: -16%">h(x)=2x^{4}-x^{2}</math>
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_4 |<span class="biglink">&nbsp;Problem 4.&nbsp;</span>]] Determine the intervals where the function&thinsp; <math style="vertical-align: -16%">h(x)=2x^{4}-x^{2}</math>
 is increasing or decreasing.
 == Marginal Revenue and Profit ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_5 |'''Problem 5.''']] Find the marginal revenue and marginal profit at <math style="vertical-align: -3%">x=4</math>, given the demand function
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_5 |<span class="biglink">&nbsp;Problem 5.&nbsp;</span>]] Find the marginal revenue and marginal profit at <math style="vertical-align: -3%">x=4</math>, given the demand function
 <math>p=\frac{200}{\sqrt{x}}</math>
@@ Line 39: / Line 39: @@
 == Related Rates (Word Problem) ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_6 |'''Problem 6.''']] A 15-foot ladder is leaning against a house. The base of
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_6 |<span class="biglink">&nbsp;Problem 6.&nbsp;</span>]] A 15-foot ladder is leaning against a house. The base of
 the ladder is pulled away from the house at a rate of 2 feet per second.
 How fast is the top of the ladder moving down the wall when the base
@@ Line 46: / Line 46: @@
 == Slope of Tangent Line ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_7 |'''Problem 7.''']] Find the slope of the tangent line to the graph of <math style="vertical-align: -14%">f(x)=x^{3}-3x^{2}-5x+7</math>
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_7 |<span class="biglink">&nbsp;Problem 7.&nbsp;</span>]] Find the slope of the tangent line to the graph of <math style="vertical-align: -14%">f(x)=x^{3}-3x^{2}-5x+7</math>
 at the point <math style="vertical-align: -14%">(3,-8)</math>.
 == Quotient and Chain Rule ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_8|'''Problem 8.''']] Find the derivative of the function <math style="vertical-align: -43%">f(x)=\frac{(3x-1)^{2}}{x^{3}-7}</math>.
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_8|<span class="biglink">&nbsp;Problem 8.&nbsp;</span>]] Find the derivative of the function <math style="vertical-align: -43%">f(x)=\frac{(3x-1)^{2}}{x^{3}-7}</math>.
 You do not need to simplify your answer.
 == Marginal Cost ==
-<span class="exam">[[022_Exam_1_Sample_A,_Problem_9 |'''Problem 9.''']] Find the marginal cost to produce one more item if the
+<span class="exam">[[022_Exam_1_Sample_A,_Problem_9 |<span class="biglink">&nbsp;Problem 9.&nbsp;</span>]] Find the marginal cost to produce one more item if the
 fixed cost is $400, the variable cost formula is <math style="vertical-align: -5%">x^{2}+30x</math>,
 and the current production quantity is 9 units.

@@ Line 13: / Line 13: @@
 == Continuity and Limits ==
-<span class="exam">Problem 3. Given a function <math style="vertical-align: -45%;">g(x)=\frac{x+5}{x^{2}-25}</math>&thinsp;,
+<span class="exam">Problem 3. Given a function <math style="vertical-align: -40%;">g(x)=\frac{x+5}{x^{2}-25}</math>&thinsp;,
-:<span class="exam">(a) Find the intervals where <math style="vertical-align: -25%;">g(x)</math> is continuous.
+:<span class="exam">(a) Find the intervals where <math style="vertical-align: -20%;">g(x)</math> is continuous.
-:<span class="exam">(b). Find <math style="vertical-align: -60%;">\lim_{x\rightarrow5}g(x)</math>.
+:<span class="exam">(b). Find <math style="vertical-align: -55%;">\lim_{x\rightarrow5}g(x)</math>.
 == Increasing and Decreasing ==