Shoreline Community College: Precalculus I - MATH 141 S2 Spring 2017
Item
1237
Dept
MATH
Num
141
Instructor: Przemyslaw Wyzgowski
Email: [email protected]
Section
S2
Cr
5
Start
0930A
End
1020A
Days
M-F
Room
2905
Start Dt
3/4
End Dt
6/16
Office: 537
Math& 264 Quiz 2 Solutions
April 20, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation
correctly. Show techniques of integration, and give simplified, exact answers. No notes are allowed.
You may not use a c
Homework 2, Part 2, Solutions
1. Use polar coordinates to find the volume of the solid that is bounded above by the paraboloid
z 1 x 2 y 2 , below by the plane z 0 , and on the sides by the cylinder x 2 y 2 x .
We express the boundary curve of the region
Math& 264 Quiz 5 Solutions
June 9, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation correctly. Give
simplified, exact answers. No notes are allowed. You may not use a calculator with a CAS (computer algebra
Math& 264 Quiz 4 Solutions
May 19, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation correctly. Give
simplified, exact answers. No notes are allowed. You may not use a calculator with a CAS (computer algebra
Homework 3, Part 2, Solutions
1. Find the volume of the solid common to the spheres 2 2 cos and 2 .
Express the sphere 2 2 cos in Cartesian coordinates:
2 2 cos 2 2 2 cos x2 y2 z 2 2 2 z
x2 y 2 z 2
2
2
Find the curve of intersection of the spheres 2 and
Homework 4, Part 2, Solutions
1
4
1. Let f ( x, y ) 8 xy ( x y ) 4 . Find all local maxima, local minima, and saddle points of f .
f ( x, y) 8 y ( x y)3 , 8x ( x y)3
f ( x, y) 0 8 y ( x y)3 8x y x
Substitute y x into f ( x, y) :
f ( x, x) 8x (2 x)3 , 8x (
Homework 1, Part 2, Solutions
ln 2 1
1. Evaluate the iterated integral:
x
0
2
2
y e y x dydx
0
For the inner integral, we use the substitution u y 2 x , and treat x as a constant. Then du 2 xydy , and we
rewrite the integrand
x 2 y e y x dy
2
1 y2 x
1
x
Homework 6, Part 2, Solutions
1. Find the surface area of that portion of the sphere x 2 y 2 z 2 9 z that lies inside the paraboloid
x2 y 2 4 z .
We complete the square in the equation of the sphere:
2
9 81
x2 y 2 z
2
4
Intersection of sphere and parabol
Math& 264 Quiz 3 Solutions
May 9, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation
correctly. Give simplified, exact answers. No notes are allowed. You may not use a calculator with a
CAS (computer algebra
Homework 5, Part 2, Solutions
1. A wire with linear density ( x, y, z) 15 y 2 kg/m lies along the curve r (t ) (t 2 1) j 2t k, 1 t 1
. Find its center of mass. Sketch the curve and its center of mass together.
First find the mass m in kg.
Units for x , y
Math& 264 Exam 2 Solutions
May 31, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation correctly.
Give simplified, exact values for problems with numerical answers. Include units with answers, where
applicable
Math& 264 Quiz 1 Solutions
April 11, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation
correctly. Show techniques of integration, and give simplified, exact answers. No notes are allowed.
You may not use a c
Math& 264 Exam 1 Solutions
May 1, 2017
Show work that is organized, complete, and mathematically precise. Use mathematical notation
correctly. Give simplified, exact values for problems with numerical answers. You may use one 4x6
handwritten note card. Yo
Homework 7, Part 2, Solutions
1. Let F ( x, y, z ) z sin x, x y 2 , y e z
and let C be the curve of intersection of the sphere
x 2 y 2 z 2 1 and the cone z x 2 y 2 , with counterclockwise orientation looking down from the
positive z-axis. Find
F dr
by us
Quiz 2
Math& 151-Version&6 Name_w_ _
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. No calculators are allowed. Please use a pencil, not a pen.
1. Evaluate the limit, or explain why it doesnt exis
Exam 2
Math& lSlVersion A Name KM
0 No calculators or notes allowed.
0 Use pencil, not pen.
0 You must show your work Wherever possible and use precise mathematical notation to receive full
credit.
1. [9 pts] Differentiate. DO NOT SIMPLIFY YOUR ANSWERS.
Math& 142 Exam 1 Solutions
February 13, 2017
Name:_
Part I No calculator
Instructions: Your work must be organized, complete, and mathematically precise. Use mathematical
notation correctly. Show complete work and simplify your final answers. No calculato
Quiz 1
Math& 151-~Verslon B Name_l'+_-.-._.
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. No calculators are allowed. Please use a pencil, not a pen.
1. The table shows the osition of a c clist a
Exam 1
Math& lSlVersion C Name W
o No calculators or notes allowed.
0 Use pencil, not pen.
0 You must Show your work Wherever possible and use precise mathematical notation to receive full
credit.
1. [9pts]Letf(x)= 16.
x_
a. Find the average rate of chang
Quiz 5
Math& 151-Version A Name_ W
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. N0 calculators are allowed. Please use a pencil, not a pen.
1. Let f and g be the functions graphed below.
a.
Quiz 4 ' \
Math& 151Version A Name Cali
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. No calculators are allowed. Please use a pencil, not a pen.
1. Differentiate each function given below. DO NO
. Sketch the graph of a function that is continuous everywhere EXCEPT atx = 2 ,
where it is only continuous from the right, and at x = -1 where there is an innite
discontinuity.
IIIIIII'
II'
7"
L
Ila-m-
gamin-
-=ll
Iliu=
5
I
I 4
III!
IIII
IIII
IIII
Math& 142 Quiz 2 Solutions
January 26, 2017
Name:_
Instructions: Your work must be organized, complete, and mathematically precise. Show complete work
and simplify your final answers. No calculators or notes are permitted.
For #1-2, sketch a graph of the
3. The graph of the function f is shown below. Use it to nd each limit. If the limit
does not exist, write does not exist or DNE. If the limit can be described using
no or oo , please use that notation. You do not need to show work for this problem.
)
J
Quiz 2
Math& 151-Version A Name_v_q4,_
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. No calculators are allowed. Please use a pencil, not a pen.
1. Evaluate the limit, or explain why it doesnt ex
Math& 142 Exam 1 Solutions
February 13, 2017
Name:_
Part 2 Using a Scientific Calculator
Instructions: Your work must be organized, complete, and mathematically precise. Use mathematical
notation correctly. Show complete work and simplify your final answe
Math& 142 Quiz 3 Solutions
February 2, 2017
Name:_
Part I No calculator
Instructions: Your work must be organized, complete, and mathematically precise. Show complete work
and simplify your final answers. No calculators or notes are permitted.
1. [3 pts]
Quiz 6
Math& 151~Version A Name LL04 _
You have 15 minutes to complete this quiz. Show your work carefully wherever possible
for maximum credit. Correct mathematical notation is required. No calculators are
allowed. Please use a pencil, not a pen.
1. On t
Quiz 1
Math& 151Version A Name _ Lgj _
You have 15 minutes to complete this quiz. Show your work carefully Wherever possible
for maximum credit. N0 calculators are allowed. Please use a pencil, not a pen.
1. The table shows the position of a cyclist at t