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Indiana - CLAS-C - 205
Classical Mythology Vocabulary: Exam 2 Look at pictures on these pages: 547-558, 394-397, 564-592, 600-614, 617-620, 621-650, 466-513, 40-54, 522-546DANAE: Daughter of Acrisius, an oracle foretold that her son would kill her father so he shut her up
Indiana - EDUC-X - 158
Mickey Green March 5, 2008 Reading Reflection #2 In the city of Dictionopolis, King Azaz's great aunt, Faintly Macabre or the "Which," is the character that chose which words the people of the kingdom would use. The townspeople would use these words
Indiana - ENG-W - 131
Mickey Green March 3, 2008 Analytical Paper What You Pawn I Will Redeem: Analysis In the short story, "What You Pawn I Will Redeem," by Sherman Alexie, a homeless Indian, Jackson Jackson, goes on a journey to reclaim his grandmother's stolen powwow r
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007 Name: Partner: . .Conundrum ConversationIn class on Wednesday I asked each of you to name two topics from among those we've talked about in class so far this semester. I first asked you to name a top
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 3This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 2This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 2This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 1, Solutions1. (15 points) Find numbers C and a such that the exponential function f (x) = Cax satisfies f (1) = 2 and f (3) = 18.2 From f (1) = 2 we have C a1 = 2, so that C = a . Fro
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 1This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Pedantic PedometersIn class we spent a little bit of time playing with the Google pedometer application, located at www.gmap-pedometer.com. This brief exercise asks you to return to that application a
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Newton v. LeibnizWho invented calculus? At the end of 1712, 46 years after Isaac Newton discovered the method, and 38 years after his rival on the European continent, Gottfried Wilhelm Leibniz, indepe
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Indeterminate FormsAs we saw on Monday, sometimes we can't really tell what a given limit might turn out to be, simply because it has a vexing indeterminate form, like " 0 ," or " inf ty ." 0 We're a
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Exam 3This practice exam is worth a total of 100 points, and point values for each question are given below. Answer every question fully and clearly. Please show all of your work where appropriate, an
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Getting Specific About Specific HeatThis first team project will ask you to work together with your group's members to develop an understanding of a certain mathematical model for specific heat, defin
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Final ExamThis final exam is worth a total of 100 points, and point values for each question are given below. Answer every question fully and clearly. Please show all of your work where appropriate, a
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.4: Limits, Done Right!If we revisit the definition of "limit" that we got from Section 2.2, we notice that there are two places where we are left guided by our intuition, rather than mathema
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Formulas and Forms: Mathematics and PoetryDoing math, to most people, is a scientific enterprise. Made up of cold lemmas, theorems, and propositions, mathematics is a means to an end, a collection of
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.5: Continuity and continuous functionsSo, you'd like to be able to work only with all of those nice functions for which the "Method of Direct Substitution" works, huh? Good news! Those are t
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.6: Limits at Infinity and Horizontal AsymptotesOkay, remember that are not real numbers, so we can't yet say limx f (x) with a straight face. But we'd like to be able to: this should, in fa
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Practice Exam 3This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Rabbit ReduxMany of you are probably familiar with the famous sequence of numbers first devised by Leonardo Fibonacci (who lived from c. 1170 to c. 1250), and named in his honor: 1. The first two term
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Assessing the Quality of Math Writing: The Four CsSo you've got to write a math paper? As such, as a very reasonable question is what makes a math paper good ? It might help you as you're writing to k
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.2: Modeling with FunctionsIn our last class we saw some examples of mathematical , functions which closely describe the behavior of "real-world" quantities or phenomena. What sorts of functi
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.3: Building New Functions from OldThere are a number of ways of constructing new functions from old ones. Today we consider some simple ways of doing this. Shifting. Given a function f , it
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.5: Fun with Exponential FunctionsIn order to understand the function f (x) = ax (here, and always, a > 0), we can play around with what ax must be for various values of x: 1. Positive intege
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.6: Inverse FunctionsIf a function f is nice enough, we may just be able to define its denoted by f -1 . If f : A B has the property that f (a1 ) = f (a2 ) implies a1 = a2 , we say that f is
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.2: The "L" Word: Limits!We need to be able to make mathematically precise the notion of "arbitrarily close, but not equal to." (We encountered this notion just a little while back when we we
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.3: Limit LawsThe book lists eleven basic properties of limits, as well as a few more theorems which should help you evaluate a large number of limits without "plugging in" or "guesstimating.
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 5.2, part II: More on Definite IntegralsnRecall thatb af (x) dx = limnf (x )x, where x is a sample point chosen i ii=1from the subinterval [xi-1 , xi ]. Our computations using Mat
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.2: Modeling with FunctionsIn our last class we saw some examples of mathematical , functions which closely describe the behavior of "real-world" quantities or phenomena. What sorts of functi
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.3: Building New Functions from OldThere are a number of ways of constructing new functions from old ones. Today we consider some simple ways of doing this. Shifting. Given a function f , it
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.5: Fun with Exponential FunctionsIn order to understand the function f (x) = ax (here, and always, a > 0), we can play around with what ax must be for various values of x: 1. Positive intege
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 1.6: Inverse FunctionsIf a function f is nice enough, we may just be able to define its denoted by f -1 . If f : A B has the property that f (a1 ) = f (a2 ) implies a1 = a2 , we say that f is
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.2: The "L" Word: Limits!We need to be able to make mathematically precise the notion of "arbitrarily close, but not equal to." (We encountered this notion just a little while back when we we
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.3: Limit LawsThe book lists eleven basic properties of limits, as well as a few more theorems which should help you evaluate a large number of limits without "plugging in" or "guesstimating.
Purdue - MA - 261
MA 261EXAM 1Form ASpring 2008Answer Key: DCAC DADB ECBB 1. Find all values of x so that the vectors a = (x, -3, 1), b = (x, x, 2) are perpendicular. The correct values of x areA. 0, 1 B. -1, 2 C. 1, 1 D. 1, 2 E. 2, 22. Determine a so that
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.4: Limits, Done Right!If we revisit the definition of "limit" that we got from Section 2.2, we notice that there are two places where we are left guided by our intuition, rather than mathema
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.5: Continuity and continuous functionsSo, you'd like to be able to work only with all of those nice functions for which the "Method of Direct Substitution" works, huh? Good news! Those are t
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.6: Limits at Infinity and Horizontal AsymptotesOkay, remember that are not real numbers, so we can't yet say limx f (x) with a straight face. But we'd like to be able to: this should, in fa
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.7: Derivatives: Instantaneous Rates of Change and Tangent LinesSo what's next? Recall that calculus is all about quantities in change, dynamic quantities. In the applications we'll soon be d
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 2.8: The Derivative, as a FunctionNow let's do what I know you've been itchin' to do for the last few classes. Notice that f gives us a rule for assigning, to any given number a, a new value .
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.1: At Last! Shortcuts!Recall the definition (and notation) for the derivative of a function f : if y = dy f (x), we can write f (x) or dx for the derivative. Our goal right now is to start d
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.2: The Product and Quotient RulesLet's continue amassing shortcuts for computing derivatives. We've now got rules for differentiating powers, as well as constant multiples, sums, and differe
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.3: Differentiating trig functionsThe goal of today's class is to nail down one particularly difficult derivative, and to derive (no pun intended!) a few others from this one: d (sin(x) = cos
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.4: The Chain Rule!The for derivatives tells us how to differentiate of functions. It is by far the most important rule for differentiation. Need proof? Have you noticed the contrived simplic
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.5: Sneakiness in Calcland: Implicit DifferentiationSometimes the relationship between two variables, x and y, say, is most easily expressed by means of a relation which is not a function. Fo
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.6: Derivatives of Logarithmic FunctionsThe astute observer may have noticed that with all we've done with derivatives, we still don't know how to differentiate logarithms. It's about time we
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.7: Another physical applicationLet's investigate one more application of calculus to physics, before we move on to talking about the way the derivative of a function tells us much about the
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.8, Applications: exponential and logarithmic modelsLet's talk a bit more about one of the most important functions in all of mathfunctions. ematics, the Such functions come up almost any tim
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 3.9 Related Rates of ChangeIn applications, one frequently deals with problems in which more than one quantity is changing with respect to change in yet another. Even if some of the rates of c
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.1: Maxima and Minima(And we ain't talkin' Nissans.) We start off with a load of. .Definitions. We say that the number c is a (or ) for the function f if f (c) f (x) for all x in f 's domain
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.2: The Mean Value TheoremToday's focus is probably the second (maybe third) most important theorem from all of calculus. (Only the Intermediate Value Theorem, which we mentioned when we defi
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.3: Derivatives and the shape of thingsWe've already seen ways in which we can tell stuff about f by examining its derivative f . For instance, if f (x) = 0 everywhere on an interval, then f
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.4: L'H^pital's Rule oWhat if we want to evaluate the limit limx1 ln(x) ? The problem here is that x-1 we have a limit of 0 in both the numerator and the denominator: the limit of the quotien
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.5: Sketchin' !With the help of calculus, we've now got several tools that'll help us understand the nature of the graph of a function f (x). Let's summarize our findings in an 8-step process
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.7: Optimizin' !Remember the Closed Interval Method, that means we developed for finding the extreme values of a given function on a closed interval? Well, how about we apply that method (and
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 4.9: Antiderivatives!For numerous reasons that will become evident next semester when you take Calc II, the ability to work backwards, obtaining a function by starting with its derivative, is
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 5.1: Areas!Today we'll work on perhaps the funnest topic of the semester. We all know how to find the area of nice rectilinear figures like squares and triangles, right? What if we're asked to
UNC Asheville - MATH - 191
MATH 191, Sections 1 and 3 Calculus I Fall 2007Section 5.2, part I: The Definite Integral, a DefinitionLet's make precise all of the whatnot we've been doing with areas, with a Definition. Let f be a function defined on the interval [a, b] and div