Worksheet #1 Midterm Review Ch. 1 + Ch. 2
Complete the following without a calculator.
Compute the following limits:
1. lim t + 2
t4
t+2
t2 t 2 4
2. lim
3. lim
x0
1 cos x
x sin x
4. lim+
x1
x +1
x 3 +1
Find the derivative usin
AP Calculus Calculator INACTIVE
Test REVIEW Chapter 1: Limits and Their Properties
Name:_
Part I: Multiple Choice: Answer the following questions in the space provided or on a separate sheet of paper
stapled to this review. SHOW ALL WORK in order to recei
Calculus Calculator ACTIVE
Test REVIEW Chapter 1: Limits and Their Properties
Name:_
Formulas and Theorems:
sin(x)
x
1 cos(x)
cos x 1
Special Trig Limits: lim
= lim
= 1 and lim
= lim
=0
x0
x0
x0
x0
x
sin(x)
x
x
Definition of Continuity: A function is cont
lim f ( x) L
Read: The limit as x approaches c of f
of x is equal to L
x c
Direct Substitution
Factor and reduce
Rationalization Technique
The Squeeze Theorem
sin x
1 cos x
lim
1 , lim
0
x 0
x
0
x
x
Note: c is an x value, and L is a y
value.
Create a tab
Calculus Maximus
Appendix A: Precal stuff to know
Stuff you need to know from Precalculus
Unit Circle
Even and Odd Functions
If f x
f ( x) , then f is an even function
If f ( x)
f ( x) , then f is an odd functions
Exponents
a 0 1, a 0
a1 a
am an am
am
am
Goldstein 1st
Gabe Goldstein
Mrs. Hammer
1st
Beta Flight Reflection
1. The most difficult part about making the parachute was cutting out the bag.
Also getting it in the best position possible. Another part was cutting string
perfect and aligned straight.
Mountain Building Study Guide:
Fill in the following notes while watching the video.
These will count as your lesson notes in lieu of a PowerPoint.
You may want to watch this video more than once in order to properly understand this material.
Geologists s
TRIG ANTIDERIVATIVES:
1) cosx dx = sinx + c
2) sinx dx = -cosx + c
2
3) tanx dx = sec x + c =
1
2
cos x
2
a. sec x dx = tanx + c
2
4) csc x dx = -cotx + c
5) secxtanx dx = secx + c
6) cscxcotx dx = -cscx + c
REIMANN SUM FORMULA:
f ( xi )
( ba
n )
lim
n
i=
BMTables.indd Page 675 11/15/11 4:25:16 PM user-s163
user-F452
Tables
Table A
Standard Normal Probabilities
Table B
Random Digits
Table C t Distribution Critical Values
Table D Chi-square Distribution Critical Values
Table E
Critical Values of the Correla
ANOVA
Analysis of Variance:
Why do these Sample Means differ as much as they do (Variance)?
Standard Error of the Mean (variance of means) depends upon
Population Variance (/n)
Why do subjects differ as much as they do from one another?
Many Random causes
Solutions to old Exam 1 problems
Hi students!
I am putting this old version of my review for the rst midterm
review, place and time to be announced. Check for updates on
the web site as to which sections of the book will actually be
covered. Enjoy!
Best,
Math 113 - Exam 1 - In-class portion - February 13, 2013
Name:
Question Number Possible Points Score
1
20
2
20
3
20
4
20
5
20
Total
100
Instructions:
Write your name on the exam now.
Dont begin until your instructor tells you to.
You may not use the book,
Math 113 - Exam 1 - In-class portion - February 14, 2012
Name:
Question Number Possible Points Score
1
20
2
20
3
20
4
20
5
20
Total
100
Instructions:
Write your name on the exam now.
Dont begin until your instructor tells you to.
You may not use the book,
Practice Sheet The Basics of Trigonometry
I. Convert the following degree measures to exact radian measures:
(1) 35 o =
(2) 150 o =
(3) 220 o =
(4) 405 o
II. Convert the following radian measures to degree measures:
(1)
2
=
3
5
=
9
(2)
(3)
7
=
18
(4)
8
=
Operations on Polynomials
I. Addition combine like terms (same variables and same exponents for these
variables) using the distributive property: ba + ca = (b+c)a
Examples: (1) 2 x 2 + 3x 2 = (2 + 3) x 2 = 5 x 2
(2) 4 xy + xy = 4 xy + 1xy = ( 4 + 1) xy =
Assignment 9 Solutions
2. The first option is better because there are more ways to win. Getting a king on
the first card and a queen on the second wins $1 under both options, but getting a
king on the first card and, say, and ace on the second card only
Assignment 8 Solutions
Ch. 11
3. (a) We use a regression where x is the height at age 6 and y is the height at age
18. The RMS error is
inches.
(b) We switch the meaning of the variables x and y. The RMS error is now
inches.
4. (a) Recall that about 2/3 o
Assignment 13 Solutions
2. (a) The sample is like 500 draws from a 0-1 box of 25,000 tickets. The number
of 1s in the sample is the number of households with internet access. The frac tion
of 1s in the box is unknown, but is estimated by the sample fracti
Assignment 7 Solutions
2. (a) We use the regression line to estimate mean values of the dependent variable
for given values of the independent variable. In this case, the regression line is
y-100 = 0.8(x-100) where y represents score at age 35 and x repre
Assignment 5 Solutions
4. (a) The corresponding z-values for 400 and 700 are (400-550)/100=-1.5 and
(700-550)/100=1.5 respectively. To use the normal approximation, we find the area
under the normal curve between -1.5 and 1.5. From the table, we see that
Assignment 1 Solutions
3. The parents who refused to allow their children to participate in the experiment
on the premise that the child would be exposed to a higher risk of polio were
incorrect. In the Salk trial, parents who consented were, on the whole
Assignment 6 Solutions
Ch. 8
1. In graph (a), the means are too low. In graph (b), the SDs are too small. In
graph (c) the SDs are too big and the correlation is too strong. The answer is
(d).
5. (i) 0.60 a moderately strong positive correlation
(ii) 0.30
Practice Midterm
All questions are worth ten points. In addition to the questions, there will
be an additional ten points to be awarded for style and clarity in writing.
1) Denitions
1. Dene the index |G : H| of a subgroup H < G.
2. Dene the external dire
Lecture 7 Notes
How to learn Abstract Algebra
Here are some remarks about how to do algebra problems.
1. When you are asked to prove a statement you must not assume that the
statement is true.
2. Never assume a group is Abelian. Some people begin their ar
Lecture 4 Notes
How to learn Proofs
HOW TO GET STARTED
Begin a proof by rewriting what you are given and what you are asked to prove
in a more convenient form. Often this involves converting word to symbols and
utilizing the definitions of the terms used
Lecture 4 Notes
How to learn Proofs
HOW TO GET STARTED
Begin a proof by rewriting what you are given and what you are asked to prove
in a more convenient form. Often this involves converting word to symbols and
utilizing the definitions of the terms used
Lecture 1 Notes
Reasons to take this class
1. Even though many students take a course is discrete math where they study
various proof techniques many of them seem not to absorb this material well.
Abstract algebra provides them much more practice at this