Limits and Continuity
1.2: Finding Limits Graphically and Numerically
The process of finding a number that you are approaching is called finding a limit. When finding limits
the domain of x does not include the number you are approaching. A limit is writt
Chapter 1
1.2: Finding Limits Graphically and Numerically
The process of finding a number that you are approaching is called finding a limit. When finding limits
the domain of x does not include the number you are approaching. A limit is written like thi
2.2 Examples: Rates of Change (velocities)
v = dt (average velocity) v (instantaneous velocity/ slope of tangent)
d
t
v =
= slope of secant
*picture*
106 p 116
A = s2
Find the rate of change of A (area) with respect to s (side) when s = 6m . Find
y=x
2
Fi
Review:
Steps for First Derivative Test:
1. Find critical numbers (Where f(x) equals zero or doesnt exist)
2. Test points around the critical numbers to see if the function changes from increasing to
decreasing
Steps for Second Derivative Test:
1. Find wh
May 2, 2016
5.5 An Important Limit
x
lim (1 + 1x )x = lim ( x+1
x )
x
x
*This function is similar to the compound interest formula
Those that are new to Calc might say that this is one. But that would be wrong because even
though the one over x is approac
3.5 Limits at Infinity
Let f (x) = an xn + an1 xn1 + . + a1 x + a0 .
Let g (x) = bm xm + bm1 xm1 + . + b1 x + b0 .
Then,
f (x)
1. lim g(x)
= if n > m .
x
lim f (x)
x g(x)
lim f (x)
x g(x)
2.
3.
=
an
bm
if n = m
= 0 if n < m
When you are looking for limits
Announcements
Week 13-14
6. Water Taxi
Max capacity is 3,500 lb. Assumed initially mean
weight of passenger 175 lb. Passenger's weight
W ~ N( 185, 41 )
a. W~N(185, 41); P(W < 175)
P(W < 175) = NORMDIST(175, 185, 41, 1)
0.40365
b. What fraction (%) of pass
Exam 2 files are uploaded - password is student ID # in gradebo
Exam 1 and 2 were about probability and descriptive statistics.
Now, we will focus on variables (Ch 5 discrete variables, Ch 6
normal distribution, Ch 7 estimation)
This unit is Weeks 9-11 Ho
Exam 2 files are uploaded - password is student ID # in gradebo
Exam 1 and 2 were about probability and descriptive statistics.
Now, we will focus on variables (Ch 5 discrete variables, Ch 6
normal distribution, Ch 7 estimation)
This unit is Weeks 9-11 Ho
Quiz 3 is Wed Apr 12
problems come from 1-5 from Week 9-11 HW
Week 9-11 HW
#5. Vegetable preferences
Out of 520 surveyed: 227 potato, 103 celery, 190 brussels
*I'm interested in pi = pop. Fraction of people prefer potat
*Since we cannot truly get pi, we m
Week 9-11 Homework
716 people randomly surveyed. The population % of pe
#1 prob at least 3 individuals have blood type O?
P(>= 3 type O)
COULD use OR rule: .=P(X=3)+P
Extra Credit M Apr 17 at 11:59 p
For this problem, why would we N
When would we use the
Announcements
Exam 3 on Mon May 8 - weeks 9-15
Quiz 4 can be any class starting today til Wed May 3
could be on any concept, problem, etc.
during the last two class periods
Project - problems 1 and 2
fraction of customers free gas = P(a customer gets free
Quiz 3 is Wed Apr 12
problems come from 1-5 from Week 9-11 HW
Week 9-11 HW
#5. Vegetable preferences
Out of 520 surveyed: 227 potato, 103 celery, 190 brussels
*I'm interested in pi = pop. Fraction of people prefer potat
*Since we cannot truly get pi, we m
Announcements
Exam 3 on Mon May 8 - weeks 9-15
Quiz 4 can be any class starting today til Wed May 3
could be on any concept, problem, etc.
during the last two class periods
Project - problems 1 and 2
fraction of customers free gas = P(a customer gets free
Central Limit Theorem
From the simulation file about the CLT, we learned a few things.
Let X have mean mu_X and standard deviation sigma_X.
We observed the distribution of x.bar.n and we saw the effect of n.
We first saw that the mean of x.bar.n is virtua
Announcements
Exam 3 on Wed May 10 on weeks 9 to 16.
Exam 4 is final exam and over select sections
*Dr H will give you the problems to study
Quiz 5 on Mon May 8 on weeks 13-14
Week 13-14 Unit
10. Doorway Height
Plane carries 100 passengers. Doors height o
Last Class
23-Jan
Statistics is in large part the study of distributions - A distribtuion is a way forto look at the frequences of X.
In other words, X = random variable and X can vary from person to
perosn and we want to know how
frequent its values are.
First Day Notes
Dr. Hussain (Dr. H), available via [email protected]
Make sure you read the course objectives and description.
At least once a day, look for any updates via email and Blackboard.
Grades
50 attendance
100 quizzes
600 exams
400 HW
150 proje
Exam 1 Redemption
Please rename the file "LASTNAME_FIRSTNAME_EXAM1_Redemption.
xlsx" and resubmit with all corrections.
If your score is low (about 60% or less), please see me after class this
week to work out a plan to rectify your grade issue.
For extra
HW WEEK 13
4/19/2017
chapter 6 (normal distribution) & chapter 7 (estimation)
In Ch 5, we finished the discrete variables unit. We saw in part
the binomial distribution: if you have n trials out of a population size of
infinity and if you have pi (populat
Announcements
Exam 1
Wed Feb 15
Weeks 1 through 4
5-10 questions inspired by homeworks
Ch 3 - Center & Variability - Final Notes
Relationship between Mean, Median, & Mode
In above figure, we have a normal distribut meaning the mean=the median=the mode
Whe
Announcements
Exam 2 moved to W Mar 22
*Homework from weeks 5 through 9*
*Bring exam questions to M Mar 20 class*
Homework 5 & 6 & 7 & 8
7 Committee problem
There are 11 people from which we have to construct
a) executive committee (pres, CEO, COO, CFO)
b
CHAPTER 3- Average and Variability
in Chapter 3 - we will describe a bit more in terms of center (i.e, mean and median) and variability (i.e, standard deviation)
In the figure above, on the right we have a sample distribution (akin to section 2.2), but on
Continuation with Week 3 & 4 Problems
6
In DrH Pick 4 lottery, you can bet $5 by selecting the exact order
of 4 digits between 0 and 9 inclusive. If you select the only one winning
arrangement of numbers, you collect $551.
a.
P(win)
If all the ways to pla
ANNOUNCEMENTS
QUIZ 1
W Feb-1- week 1 hw
*HW WEEK 1 Due Wed Feb 1.
EXTRA CREDIT (1 pt each) due 11:59 pm., Feb 1.
write answers out in your own words and then copy and paste the webs
1 Provide 3 sources that give the cost of pure black ink per gallon.
2 Pr
@ MaerlngBiotogy: Checkpoints , Lecture is , Google Chrome
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MCB 250 FA16 (SlauchlShankIand)
SEEM": , Lecture 16 Pat 6-6
ReworklolPlactice em. compleledlhis assignment - i 1 am
Finite Math 1553 Project 1
The Method of Least Squares
Zainulabidin Adhami
October 6, 2016
1
Amount Spending on Advertising (in
thousands)
x
10
11
17
14
18
21
15
20
19
22
Weekly Sales Volume (in thousands)
y
50
55
61
52
65
75
60
65
62
77
2
Amount Spent on