Math 252
Name: _
QUIZ 3 (SECTIONS 16.3-16.9)
MATH 252 FALL 2007 KUNIYUKI
SCORED OUT OF 125 POINTS MULTIPLIED BY 0.84 105% POSSIBLE
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Math 252
Name: _
QUIZ 3 (SECTIONS 16.3-16.9)
MATH 252 FALL 2008 KUNIYUKI
SCORED OUT OF 125 POINTS
MULTIPLIED BY 0.84
105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes o
Math 252
Name: _
QUIZ 4 (CHAPTER 17)
MATH 252 FALL 2007 KUNIYUKI
SCORED OUT OF 125 POINTS MULTIPLIED BY 0.84 105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
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Math 252
Name: _
QUIZ 4 (CHAPTER 17)
MATH 252 FALL 2008 KUNIYUKI
SCORED OUT OF 125 POINTS
MULTIPLIED BY 0.84
105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes or books
Math 252
Name: _
QUIZ 5 (CHAPTER 18)
MATH 252 FALL 2006 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes or books allowed. A scienti
Math 252
Name: _
QUIZ 5 (CHAPTER 18)
MATH 252 FALL 2008 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes or books allowed. A scienti
How do you graph the surface z = sin 2 over the annulus R from our example in
the 17.3 notes? How would you graph the corresponding solid whose volume we
were finding?
First off, lets consider the graph of sin 2 vs. in Cartesian coordinates:
The square of
Math 252
Name: _
QUIZ 2 (CHAPTER 15, 16.1, 16.2)
MATH 252 FALL 2008 KUNIYUKI
SCORED OUT OF 125 POINTS
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Math 252
Name: _
QUIZ 2 (CHAPTER 15, 16.1, 16.2)
MATH 252 FALL 2007 KUNIYUKI
SCORED OUT OF 125 POINTS MULTIPLIED BY 0.84 105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
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No not
x2 + y2
z2 = 1
A Hyperboloid of One Sheet
Traces in x = k (Hyperbola class):
Traces in y = k (Hyperbola class):
Traces in z = k (Ellipse / Circle class):
JUMBLING TSPs
How is (a b) c related to (a c) b ?
Determinant approach:
a1 a2
(a b) c = b1 b2
c1 c2
a3
b3
c3
a1
(a c) b = c1
b1
a3
c3
b3
a2
c2
b2
The determinant forms differ only by a single switch of two rows, so
they differ only by a sign.
(a b) c = -
Find
y
of the following
(remember, x acts like a
constant):
1) ex x y2
2) y2ex2 y3
y2
3)
ln y
4)
cos3 xy2
5) tan-1( xy2)
6) sin3 y
7) sin
y3
8) ln x2 + y2
Answers
(not necessarily simplified):
ex x y2 = ex x (2 y)
1)
y
ex x acts like a constant multip
16.3: PARTIAL DERIVATIVES
(Mathematica was used to produce these computer graphics.)
Note: The coordinate axes are oriented in an unusual way:
The large black dot indicates the point (1, 2, 3).
Figure #1: Graph of f ( x, y) = -5 x 2 + y3
Figure #2: The ta
Math 252
Name: _
QUIZ 1 (CHAPTER 14)
MATH 252 FALL 2007 KUNIYUKI
SCORED OUT OF 125 POINTS MULTIPLIED BY 0.84 105% POSSIBLE
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Math 252
Name: _
QUIZ 1 (CHAPTER 14)
MATH 252 FALL 2008 KUNIYUKI
SCORED OUT OF 125 POINTS
MULTIPLIED BY 0.84
105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes or books
Math 252
Name: _
QUIZ 1 (CHAPTER 14)
MATH 252 FALL 2008 KUNIYUKI
SCORED OUT OF 125 POINTS
MULTIPLIED BY 0.84
105% POSSIBLE
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers!
No notes or books
QUIZ 1 (CHAPTER 14) - SOLUTIONS
MATH 252 FALL 2007 KUNIYUKI
SCORED OUT OF 125 POINTS MULTIPLIED BY 0.84 105% POSSIBLE
Clearly mark vectors, as we have done in class. I will use boldface, but you dont!
When describing vectors, you may use either
or i j k n
QUIZ 1 (CHAPTER 14) - SOLUTIONS
MATH 252 FALL 2008 KUNIYUKI
MULTIPLIED BY 0.84
SCORED OUT OF 125 POINTS
105% POSSIBLE
Clearly mark vectors, as we have done in class. I will use boldface, but you dont!
When describing vectors, you may use either
or i j k n
SOLUTIONS TO THE FINAL
MATH 252 FALL 2008 KUNIYUKI
60 POINTS TOTAL (15 PROBLEMS; 4 POINTS EACH)
No books allowed. An appropriate sheet of notes and a scientific calculator are allowed.
1) If a and b are vectors in V2 such that a b < 0 , which of the follo
Quiz 5 R1
REVIEW: CH. 18
Here, we deal with Cartesian coordinates. (Schey and Marsden discuss other systems.)
VECTOR FIELDS (18.1)
We say a scalar function f is nice if its 1st-order partial derivatives are continuous
(and, therefore, f itself is) where w
SOLUTIONS TO THE FINAL
MATH 252 FALL 2006 KUNIYUKI
60 POINTS TOTAL (15 PROBLEMS; 4 POINTS EACH)
No books allowed. An appropriate sheet of notes and a scientific calculator are allowed.
1) What is the geometric definition of the dot product of two vectors