Math 203: HW 4
Due on Thursday, June 6
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 4
Problem 1
For the following functions give the interval(s) of increasing/decreasing and concavity, critical points, inection points,
Math 203: HW 11
Due on Thursday, June 27
Summer 12
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 12 ): HW 11
Problem 1
Let f (x, y) = exy + ln(xy) + y 3 + x3 . What is
f
x
and
f
y ?
What is
2f
xy ?
Problem 2
Let f (x, y) = x2 + y 2 + 15x
Math 203: HW 6
Due on Thursday, June 13
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 6
Problem 1
You have been asked to design a can (in the shape of a right cylinder, with a top and a bottom). You have
been told that
Math 203
Midterm Review
Corrections/alterations have been marked by larger font and a .
(1) (10 points)
Using the limit denition of the derivative, give f (x) if
f (x) =
f (x) =
x2
1
+1
1
x3
f (x) =
x
f (x) = x2 + 5x
2
(2) (10 points) Compute
lim
x9
lim
Take Home Final - 203 Summer 11
John Clark Robertson
Manapua Food Truck
We are considering where to open up a manapua truck in three dierent locations. Site A has a manapua
s
demand equation of p(s) = 10e 1000 and a per manapua tax of 10 cents. Site B has
Math 203
Quiz #1
Problem 1: Find the domain of the following functions:
a) = ! + 10 + 28
b) =
c) =
! ! !
!
!
d) = ! ! !
Problem 2: Find the x-intercept(s), and y-intercept of the following functions:
a) 6 + 13 = 1
b) y = ! 4 + 4
Problem 3: Calculate the
Math 203
Quiz #2
Problem 1: Compute the following. (For the limit questions: if the limit is
write this).
a)
b)
!
(27
!"
!
!
!
(9 ! + 7 !
!"
!
!
)
c) ! If = 2 5 !
!
d) The formula for acceleration of a particle, given its velocity is
= ! 4 ! + 120
e)
Math 241: HW 10
Due on Wednesday, June 28
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 241 ( Summer 13 ): HW 10
Problem 1
Revolve f (x) = sin(x) on [0, ] about the x-axis and nd the volume of the resulting solid. You may use the
fact that
Math 203: HW 8
Due on Tuesday, June 18
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 8
Problem 1
Evaluate the following indenite integrals (remember, this means to nd an antiderivative):
3x3 + 2x + dx
1+ x
dx
x
hint: do
Math 203: HW 3
Due on Tuesday, June 4th
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 3
Problem 1
Graph the following functions and give the domain and range:
1
f (x) =
x2
1
: x<1
: 1 x 1
: x1
1
: x<1
: 1 x 1
: x1
g(x
Math 203: HW 7
Due on Fiday, June 14
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 7
Problem 1
Assume that population growth satises the dierential equation P (t) = kP (t). (note that this means that
P (t) = ekt for som
Math 203: HW 1
Due on Wednesday, May 23
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 1
Problem 1
Let P1 = (1, 3) and P2 = (2, 5). Give the equation of the line that hits P1 and P2 .
Problem 2
Graph g(x) = x2 . Include
Math 203: HW 3 (redo)
Due on Wednesday, June 12th
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 3 (redo)
Problem 1
Graph the following functions and give the domain and range:
2
f (x) =
x2 + 1
2
g(x) =
2
2
x
2
: x < 1
Math 203: HW 5
Due on Wednesday, June 12
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 5
Problem 1
Consider the implicit function
y 4 x 4y 2 x = 3
Show that the point (1, 1) is indeed on the graph and give the equation
Math 203: HW 2
Due on Friday, May 31
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 13 ): HW 2
Problem 1
Give the domain and range of the following functions:
f (x) = x2
g(x) =
h(x) =
3
x
3
x2 + x 2
j(x) =
x2
1
+x2
Problem 2
Fin
Math 241: HW 9
Due on Tuesday, June 27
Summer 13
John Curlee Robertson
1
John Curlee Robertson
Math 241 ( Summer 13 ): HW 9
Problem 1
Use U -sub to compute the following:
(x3 + 3x2 + 3)10 (x2 + 2x) dx
sin( x)
2 x
x1
(x + 1)4
dx
dx
/4
sec2 (x2 )2x
dx
0
Pag
Math 203: HW 12
Due on Friday, June 28
Summer 12
John Curlee Robertson
1
John Curlee Robertson
Math 203 (Summer 12 ): HW 12
Problem 1
Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second
derivative test to
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by Ca
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by Ca
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 6 Solutions
#1
Integrate:
4 x3
(a)
3 x2
2x
1 dx
(b) sin 2 d
(c) sec2 3 t dt
Solution
(a)
4 x3
3 x2
2x
x4
1 dx
x3
x2
x
C.
(b)
1
2
cos 2
1
3
sin 2 d
tan 3 t
C.
(c)
sec2 3 t dt
C.
#2
Integrate:
1
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 7
#1
Evaluate the following indefinite integrals.
(a) x ln x dx
(b)
x3
x2
x cos x dx
(c) x2 sin 2 x dx
(d) x3 e3 x dx
Solution
(a) Integration by parts with u
ln x and dv
x2
2
x ln x dx
x2
2
x3
MATH 203 - Summer 2014
Instructor: Patrick Collins
Trigonometry Notes
Radians
An angle , measured in radians, corresponds to an arc length of on the unit circle. Angles are measured from the
positive real axis.
1
1
1
1
Thus we have:
360
180
90
2 radian
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 4 Solution
For each problem an equation and a point are given, along with the graph of the equation and the tangent line to the
graph at that point. Do the following.
(a) Verify that the point l
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 3
In each problem you are given a function f x . For each, do the following:
(a) Identify the domain and any intercepts.
(b) Find f x and f x .
(c) Find all critical points. (You must find the y
MATH 203 - Summer 2014
Instructor: Patrick Collins
Exam #2 Solutions
#1 (10 pts - 5 pts each)
Differentiate the following functions. Use Leibniz notation (i.e.
(a) y
x3 sin x2
1
(b) r
tan2 3 5
5 3
dy
dx
instead of y )
2
Solution
(a)
dy
dx
3 x2 sin x2
1
2
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 1
#1
Write each linear equation in slope-intercept form, and identify the slope and y-intercept.
(a) 8 x
y
3x
(b) 10 y
3
(c) 7 x
4y
6x
4
6y
(d)
5
4
x
3y
(e)
2
3
y
x
8
x
10 x
3x
2y
1
2
7
5y
4
7
5
MATH 203 - Summer 2014
Instructor: Patrick Collins
Worksheet 1
#1
Find the derivative of the following functions.
1
f x
4
2
8
4 x3
y
y
19
y
2
f x
x
f x
9
2 x3
y
10 x5
6 x2
2
12
5x
3
x
2
y
y
8
5 x x2
12
4
5 x2
y
15
y
10
17
y
26
x2
y
23
3
18
2 x3 4 x2 3
20