Perspective Approach to Culture
When we follow the Wire in society, we
feel like were an accepted part ofthe
Structural group. This creates a sense ntsocial
Functionalism 3"
The norms in our society tend to reect
the norms olthe people with the most
Conir
Definition of a Limit
: If the values of f(x) can be made as close as we like L by taking values of
x sufficiently close to a ( but not = a) then we write limx->af(x) = L which is read The limit of f(x)
as x approaches a is L
Limits fail for the following
Example of Chi^2
Initial Spreadsheet
For 100 M&M's
df = 4 - 1 = 3
Groups of Observed and Expected Data
Red
Brown Yellow Green
Groups
25
15
15
Observed 45
40
30
20
10
Expected
Enter alpha 0.050
(45-40)^2/4(25-30)^2/30(15-20)^2/2(15-10)^2/1
= ^2 cal
5.21 ad
ASTR 105 ASTRONOMY TEST 2 STUDY GUIDE
Chapter 3: Important Concepts and Skills
Understand how the ancients attempted to explain apparent retrograde motion, culminating in
the Ptolemaic model.
Be familiar with the distinct contributions of the thinkers/sci
Teresa Rocha
3-31-2013
Extra Credit
On March 28th two great men and mathematicians came to the University of North
Carolina in Asheville and debated the significance of pi versus that of e. These men fought long
and arduous debates proving their points on
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 5.2, part I: The Definite Integral, a Definition
Let'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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 4.4: L'H^pital's Rule o
What 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 4.3: Derivatives and the shape of things
We'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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 4.2: The Mean Value Theorem
Today'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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.9 Related Rates of Change
In 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.8, Applications: exponential and logarithmic models
Let'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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.7: Another physical application
Let'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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.6: Derivatives of Logarithmic Functions
The 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.5: Sneakiness in Calcland: Implicit Differentiation
Sometimes the relationship between two variables, x and y, say, is most easily expressed by means of a relation which is not a function. Fo
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.3: Differentiating trig functions
The 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 3.2: The Product and Quotient Rules
Let's continue amassing shortcuts for computing derivatives. We've now got rules for differentiating powers, as well as constant multiples, sums, and differe
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 2.8: The Derivative, as a Function
Now 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 .
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 2.7: Derivatives: Instantaneous Rates of Change and Tangent Lines
So what's next? Recall that calculus is all about quantities in change, dynamic quantities. In the applications we'll soon be d
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 2.6: Limits at Infinity and Horizontal Asymptotes
Okay, 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 2.5: Continuity and continuous functions
So, 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 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
MATH 191, Sections 1 and 3 Calculus I Fall 2007
Section 2.3: Limit Laws
The 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.