Max and Quasi Linear Concave
1. these are all or nothing problems so demand will be 0 for nothing and m/p
for other
2. check if mu of both x and y are integers, if so you can take shortcut and solve
as a perfect substitutes problem
3. If not then you will
Perfect Substitutes
1. this means that it is an all or nothing problem so demand is either 0 if none is
being consumed or m/p if all is being consumed
2. This also means that you dont have to compare utilities b/c marginal utility
doesn have a variable in
Practice for Test #1
Exam 2 Review:
Set up integrals for the following problems. You will only need to evaluate an integral for 8.5
6.1 The graphs of y = sin( x ) and y = cos x , x = 0 and x = 2 form two regions. Find the area of first region
using vertic
Recall the same picture was used for problems 1-5.
1. Set up an integral to determine the area bounded by the graphs of x = 5 y y 2 and y = x . You do not need
to evaluate your integral. (10 points)
4
( 5y y
0
2
)
y dy
2. The region in problem 1 (betwee
Math 3B (Smith)
First Exam
Name:_
(Last name, first name)
1. Evaluate the integrals (3 points each)
a)
1 x 2 dx
5x2 3x + 2
b) 3
dx
x 2 x2
c) sin 2 (2 x) cos 2 ( 2 x ) dx
d)
1
x 2 2 x + 17
dx
e)
x
2
ln x dx
f) sin 2 (2 x) cos3 ( 2 x ) dx
2. The graph of y
Practice for Test #1
7.1 a)
7.2 a)
7.3 a)
7.4 a)
x 2 cos x dx
b) sin 1 x dx
c) e x cos x dx
sin x cos3 x dx
b) sin 4 x dx
c)
tan
9 x2
dx
x2
b)
c)
c)
x4 + 1
x5 + 4 x3 dx
0
1
( x + 4 ) ( x 1) dx
b)
x
1
2
dx
2
x +4
2 x2 x + 4
x3 + 4 x
3
sec d
x
dx
3 2 x
Practice for Test #1
7.1 a)
0
(
)
x 2 cos x dx = x 2 2 sin( x ) + 2 x cos( x )| = 2
b) sin 1 x dx = x sin 1 ( x) + 1 x 2 + C
( Parts twice: u = cos x, then u = sin x.
7.2 a)
sin x cos3 x dx = 23 sin
b) sin 4 x dx =
1
32
(Integration by parts twice, u = x
Math 3B (Smith)
First Exam, part 2
Name:_
(Last name, first name)
3. Recall problem 2 from the last exam. The graph of y = f ( x) was
Algebraically, f ( x) = 12 x 2 12 x + 1
a) By using the appropriate error formula, give an upper bound on the error in yo
Math 13 - Homework 1
Name: _ Class Number: _
1) In a statistical study what is the difference between an individual and a variable?:
2) Explain the meaning of:
a.
b.
c.
d.
qualitative variable.
quantitative variable.
discrete, quantitative variable.
conti
Section 1.1
4. A parameter from a given population
never changes. Data from samples may
vary from sample to sample, and so
corresponding sample statistics may
vary from sample to sample.
(3) Nominal level.There is no apparent
order relationship among resp
ale
swim:
74PM , 1'2?“
Fall 201 5
BERKELEY CITY COLLEGE _
MATH 13- Introduction to Statistics Section B7- 40862 Lecture 4 units
Saturday 9:00 AM-12:50 PM room BCC 055
Prerequisites: Math 203 Intermediate Algebra
Course description and program: _ .
0 Intro
Precalculus (25125) ( Math 1 ) HW Set #7.
Due Wednesday, March 19th.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write th
Precalculus (25125) ( Math 1) HW Set #2.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write the correct answer to demonstr
Precalculus (25125) ( Math 1) HW Set #4.
Due Wednesday, February 26th.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write t
Precalculus (25125) HW Set #1. In order to receive a , you must attempt all problems and write out all
steps leading to your answers neatly and legibly. You cannot simply write the correct answer to
demonstrate your
Precalculus (25125) ( Math 1 ) HW Set #5.
Due Wednesday, March 5th.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write the
Precalculus (25125) ( Math 1 ) HW Set #6.
Due Wednesday, March 12th.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write th
Precalculus ( Math 1 ) HW Set #9.
Due Wednesday, April 23rd.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write the correc
Precalculus (25125) ( Math 1 ) HW Set #8.
Due Wednesday, April 9th.
In order to receive a , you must attempt all problems and write out all steps leading to your answers
neatly and legibly. You cannot simply write the