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Math 30 Calculus Wednesday, 4 May 2016
Quiz #7 '
Name:
(10 points each)
1) Find the antiderivative.
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Math 30 Solutions to take-home ortion of the Final Exam
Evaluate each limit.
a. _ x48x3+15x2
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Problem Solving Rubric
Excellent
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A
The solution is
logical, thorough,
organized, and
easy to read,
including written
explanations if
necessary to clarify
work.
The solution
includes any
diagrams, graphs,
tables, or other
supplements
needed t
Name
Math 21
Fall 2016
Exam 2
Round all appropriate answers to six decimal places and let any K values be the least
integer that works. See page 6 for error bound formulas and an integral table.
1. Evaluate each of the following integrals.
a) (9 pts.)
x2
1
FUNCTIONS AND MODELS
1.1 Four Ways to Represent a Function
In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here.
1. (a) The point (1, 2) is on the graph of f , so f (1) = 2.
(b) When x = 2, y i
Name
Math 21
Fall 2016
Exam 4
1. (8 pts.) Find the rectangular equation of the curve whose polar equation is
r 4sin 2 cos . Your answer should not contain any inverse trig functions and should look
like a familiar type of curve.
2. (8 pts.) Find the value
Name
Math 21
Exam 1 No calculators
1. Evaluate each of the following integrals.
x 2 3 x 4 dx
a) (6 pts.)
x2
/2
cos x dx
b) (7 pts.)
0 1 sin 2 x
c) (8 pts.)
x sec
2
x dx
Fall 2016
2
d) (8 pts.) arcsin x dx
e) (7 pts.) sin 6 x cos3 x dx
f) (7 pts.) sec
Name
Math 21
Fall 2016
Exam 3
1. (8 pts.) Find the centroid of the region bounded by y 1 x 2 and the x-axis. Express your
answer with fractions in lowest terms.
2. (8 pts.) A certain species of bird has an average lifespan of 3.2 years with a standard dev
HAVE YOUR PHOTO ID OUT. Ill EITHER COME AROUND THE ROOM TO PUT NAMES ON EXAMS,
OR PUT YOUR NAME ON THE EXAM WHEN YOU TURN IT IN.
You may use the backs of the exam pages and the bottom of this page for scratch paper, but may not use scratch
paper that you
Ive decided to make half of Exam #3 take-home.
Making this exam take-home, makes this an open book, open note test.
Though I have no way to monitor or prevent you from getting help on
this take-home part of the exam, it would certainly be very suspicious
Study Guide and Exam Information for Math 011 Exam 3
For your 3rd exam, you have five options regarding when to take the exam. All exams will
be given on the Vallejo campus Wednesday-Thursday, November 9th-10th.
Wednesday afternoon exam option: 3:30-5:50
Math 011- Exam #1
FORMULA and COVER SHEET
DONT PUT YOUR NAME ON THE FIRST EXAM PAGE. When you finish the exam, bring it up to me to turn it
in. If I have not already checked your ID and put your name on the exam, Ill do so when you turn it in.
You may use
The first four sheets are directions, formulas, and tables. They may be removed.
Exam pages 1-8, containing questions 1-4 were posted on Canvas, passed out in class when you turned in
Exam #2, and/or emailed to you in March. You should have turned these i
EXAM #1 information:
Your exam will take place on Thursday, September 8th
All exams will be given on the Vallejo campus.
You may choose the other time slot that fits your schedule better.
Morning exam option: 9:30 a.m.-11:50 p.m. in room 242
Afternoon exa
Study Guide and Exam Information for Math 011 Exam 2
NOTE THAT SOME OF THESE HAVE CHANGED
since the syllabus was first published.
The 2nd exam will take place on
Wednesday-Friday, October 5th, 6th, and 7th
All exams will be on the Vallejo campus. You may
Section 5.2: The Definite Integral
Def
Math 20
Let f be a function defined on [ a, b ] where [ a, b ] is divided into n subintervals of equal width. Let
x1 , x2 ,.xn be any sample points in the subintervals. Then the definite integral of f from a to b is
Section 5.3: The Fundamental Theorem of Calculus
Suppose f is a continuous function on [ a, b ] . Define a new function for area.
Math 20
g ( x) = f (t )dt
x
a
Example
Show f ( x) = x on [1, 4]
Fundamental Theorem of Calculus Part I
Suppose f is continuou
Section 5.5: The Substitution Rule
If f ( x) = e x , what is f ( x) ?
2
Math 20
f ( x) = _. Thus
But how do we do this from the integral side? We can use the _ method.
2
2 xe x dx
How to choose u ( x) : Pick the piece of the integral that you have the der
Section 5.1: Areas and Distance
Math 20
Example Find the area under the curve of y =
2
x from 0 x 3 .
3
Area =
Example Find the area under the curve of y = x 2 from 0 x 1 .
For this function we will need to
_ the area.
We _ the interval [ 0,1] into
four _
Section 4.1: Maximum and Minimum Values
Math 20
Def
A function with domain D has an absolute (or global) maximum at c if f ( c ) f ( x ) for all x in
Def
A function with domain D has an absolute (or global) minimum at c if f ( c ) f ( x ) for all x in
D.
Rolles Theorem Let f be a function such that
1) f is continuous on a, b .
2) f is differentiable on a, b .
3) f a
f b
In this case, there is a number c in a, b with f c
0.
Proof:
If f is a constant, then c can be any number in a, b .
If _ for some x in a,
Section 5.4: Indefinite Integrals and the Net Change Theorem
Math 20
Def An antiderivative of f is denoted
This is called the _ integral.
f ( x)dx
Note:
1)
f ( x)dx
is a _ whose derivative is _.
b
2)
is a _ with various interpretations: _
a
f ( x)dx =
Written Homework 5 Math 330 Fall Name: [/qu cfw_35533. RQJL'ILS
This assignment is based on lessons 1720.
1) You want to write a function, x], to represent the money in an inheritance
account. Every year since the account was started [it was started in 20
Written Homework 1 Fall Math 330 Name:
% meme:
This written homework is based on lessons 14.
1. Simplify the following: You must Show your work in a neat and orderly
fashion and do not skip steps. I want you to Show each equivalent expression
below the pr
Section 3.1: Derivatives of Polynomials and Exponential Functions
Math 20
Properties:
1) If f ( x) = c and c is a constant, then f '( x) = _ .
2) If f ( x) = x then f '( x) = _ , or
d
( x ) = _ .
dx
Try to find the pattern.
If f ( x) = x 2 , then f '( x)
Section 1.1: Four Ways to Represent a Function
Math 20
Question: What is Calculus?
Answer: The study of how things _.
There are two basic areas:
1) Velocity -
Recall: Distance = _
a)
b)
This graph shows a _ rate/slope.
But what is the rate/slope of this g
Section 5.1: Areas and Distance
Math 20
Example Find the area under the curve of y =
2
x from 0 x 3 .
3
Area =
Example Find the area under the curve of y = x 2 from 0 x 1 .
For this function we will need to
_ the area.
We _ the interval [ 0,1] into
four _
Section 4.1: Maximum and Minimum Values
Def
Math 20
A function with domain D has an absolute (or global) maximum at c if f ( c ) f ( x ) for all x in
D. f ( c ) is called a maximum value of f on D.
Def
A function with domain D has an absolute (or global)