MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic].
First find the derivative of the function[pic], f ’(x):
[pic] = [pic] apply power rule of differentiation   = [pic] simplify   = [pic] finish simplifying by first factoring     out GCF   = [pic] next factor the trinomial factor,     leaving the final simplified form of     the derivative 
Set[pic]and solve for x to find critical point(s):
When the derivative is set to zero, [pic]; thus, this implies each factor could be equal to zero, meaning that there could be up to three values for x.
[pic] = [pic] set first factor equal to zero  [pic] = [pic] divide each side of the equation by 2 [pic] = [pic] simplify to find first value of x 
[pic] = [pic] set second factor equal to zero  [pic] = [pic] add 3 to each side of the equation  [pic] = [pic] simplify to find second value of x 
[pic] = [pic] set third factor equal to zero  [pic] = [pic] subtract 2 from each side of the     equation  [pic] = [pic] simplify to find third value of x 
Therefore, the xcoordinates of the relative extreme points are in the following set: [pic].
Answer is D 
2) A manufacturer estimates that the profit from producing x units of a commodity is[pic]dollars per week. What is the maximum profit he can realize in one week?
A) $300 
B) $400 
C) $500 
D) $275 
E) none of these 
[pic]
First find the derivative of the profit function[pic], P’(x):
[pic] = [pic] apply power rule of     differentiation   = [pic] simplify 
Set[pic]and solve for x to find critical point(s):
...
QoS Techniques: MPLS
CET 2486C – Network Technologies
Professor:
November 27, 2012
Abstract
MPLS or Multi Protocol Label Switching is a networking technology that functions between layers 2 and 3 of the OSI model. MPLS constitutes of adding a label (sometimes called “Shim” because of their placement between layer 3 and layer 2 headers.) to the data package, this label contains special addressing and sometimes prioritization information. Because the MPLS label contains all the information necessary for the router to forward the package to the next hop, the router does not have to spend time analyzing the entire package thus improving network latency or bottlenecks. Due to its multi protocol capabilities MPLS can be integrated with different networking technologies from ATM to native IP environments; in addition, this multi protocol capability also provides a way to converge different types of traffic such as data, voice and video onto one network. MPLS technology also provides some other advantageous features like Traffic Engineering (TE), VPN, Any Transport over MPLS (AToM) and Quality of Service (QoS). This paper will help provide an understanding of how MPLS works and the QoS capabilities it can provide.
History of MPLS
In 1996 a group from Ipsilon Networks introduced a “flow management protocol”, this technology only worked with ATM transmissions and did not become very popular in the...
...Calculus
is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem ofcalculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a welldefinedlimit. Calculus has widespread uses in science, economics, and engineering and can solve many problems that algebra alone cannot.
Calculus is concerned with comparing quantities which vary in a nonlinear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.
BRANCHES OF CALCULUSCalculus is concerned with comparing quantities which vary in a nonlinear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If...
...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Prerequisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
11.
12.
Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
13.
Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting Transformations, combinations,...
...1.  Question :  Language performs a ________________, which means it allows you to explore and investigate the world, solve problems, and learn from your discoveries and experiences. 

 Student Answer:   Personal function 
   Interactional function 
   Ritual function 
   Heuristic function 
 Instructor Explanation:  The answer can be found in Section 4.2 of Making Connections. 


 Points Received:  1 of 1 
 Comments:  


2.  Question :  One reason language is so powerful is that it is the means by which you construct your reality. 

 Student Answer:   True     False 
 Instructor Explanation:  The answer can be found in Section 4.4 of Making Connections.     
    

 Points Received:  1 of 1 
 Comments:  


3.  Question :  The part of the body where emotions are primarily expressed is a person’s _____________, although other nonverbal channels such as vocal sounds, posture, and hand gestures can contribute information about the intensity of the emotion. 

 Student Answer:   Heart 
   Clothes 
   Face 
   Height 
 Instructor Explanation:  The answer can be found in Section 5.3 of Making Connections. 


 Points Received:  1 of 1 
 Comments:  


4.  Question :  Body posture is NOT an indicator of how interested you are...
...Calculus I Midterm 2
November 2013
2
1. (6 marks) Find the following limit:
lim (1 + sin 7 x )
cot 5 x
x →0 +
(
2. (3 marks) Find the derivative of y = 3 x + 5
2
)
sec x
Calculus I Midterm 2
November 2013
3
3. (Total 8 marks) Answer each question in the space provided. Do NOT simplify your
answer.
x2 − x
3
dy
of the function f ( x) = ln( x3 )
a) Find
dx
e
[
( )]
b) If f ( x) = arcsin x
c) Find
( (
d
sin 2
dx
d) If f ( x) =
1
4 x
3
4
+ π 2 , find f ′(x)
tanh (x )
+ (2 x )
))
1
−e
2
(2 marks)
(2 marks)
(2 marks)
− log 7 (8 x) , find f ′(x )
(2 marks)
Calculus I Midterm 2
November 2013
4
4. (2 marks each; total 10 marks) For each of the following questions, select the
correct answers by clearly shading in the appropriate boxes. Each question is worth 2
marks, but there may be anywhere from 0 to 4 correct answers. You will lose marks for
each incorrect choice (i.e. selecting something that’s wrong, or missing something that’s
correct, up to a maximum of 2 marks deduction per question (i.e. no negative marks ☺)
a) L’Hospital’s rule can be applied to which of...
...1. ht= 4.9t2+ 450, where t is the time elapsed in seconds and h is the height in metres.
a) Table of Values
t(s)  h(t) (m) 
0  ht= 4.9(0)2+ 450= 450 
1  ht= 4.9(1)2+ 450= 445.1 
2  ht= 4.9(2)2+ 450= 430.4 
3  ht= 4.9(3)2+ 450= 405.9 
4  ht= 4.9(4)2+ 450=371.6 
5  ht= 4.9(5)2+ 450=327.5 
6  ht= 4.9(6)2+ 450= 273.6 
7  ht= 4.9(7)2+ 450= 209.9 
8  ht= 4.9(8)2+ 450= 136.4 
9  ht= 4.9(9)2+ 450=53.1 
10  ht= 4.9(10)2+ 450= 40 
b) Average velocity for the first 2 seconds after the ball was dropped=
h2h020 = 430.445020 = 19.62 = 9.8 m/s
c) Average velocity for the following time intervals:
i. 1≤t≤4 = h4h141 = 371.6445.141 = 73.53 = 24.5 m/s
ii. 1≤t≤2 = h2h121 = 430.4445.121 = 14.71 = 14.7 m/s
iii. 1≤t≤1.5 = h1.5h11.51 = h1.5=4.91.52+450445.11.51 = 438.975445.11.51
= 6.1250.5 = 12.25 m/s = 12.3 m/s
d) Instantaneous velocity at t= 1 second = h1h0.7510.75 = 445.1 h0.75= 4.90.752+ 45010.75 = 445.1447.210.75 = 2.10.25 = 8.4 m/s
FIND GRAPH ON FOLLOWING PAGE
2. M=10.50.4t2, where M is the mass in grams and t is the time in seconds.
a) All the sugar has dissolved when M= 0 g...
...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem ofcalculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a welldefined limit. Generally considered to have been founded in the 17th century by Isaac Newton and Gottfried Leibniz, today calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot.
Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of...
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