Math 340, Jerey Adams
Test I, November 19, 2010
For complete credit you must show all work
Question 1 [15 points] Let f (x, y ) =
2xy
.
x2 y 2
(a) Compute f (x, y )
(b) For what values of x, y is the function f not invertible near (x, y ).
Question 2 [10]
Math 340, Jerey Adams
Test I, December 6 , 2010
TAKE HOME - Due Wednesday December 8 in class
Solutions
Question 1 This is obviously innite.
Question 2 Surprisingly it is easier to do it in vertical slices.
y = 3x+1
x=0
y = 3x+1
1
x= 3
0
=
1
3
=
1
2
y = 3
Math 340, Jerey Adams
Test I, November 19, 2010
For complete credit you must show all work
Question 1 [15 points] Let f (x, y ) =
(a) f (x, y ) =
2xy
.
x2 y 2
2x 2y
2x 2y
(b) The determinant is 4y 2 4x2 = 4(x2 + y 2). This equals 0 only if
x = 0, y = 0, s
MATH 340 EXAM 2
NOVEMBER 17, 2009
1.(15) A bug is crawling on a piece of heated graph paper and notices
that if it moves in the positive x-direction it heats up by 2 deg and if
cm
it moves in the positive y -direction it cools down by 3 deg . In which
cm
5662/7
MATH 340: Final December 17, 2011 6- (013625
§C+m~02ot
Answer each numbered problem on a separate answer sheet, and write your name
and problem number on each sheet. Show all work. When you are done, arrange
the answer sheets in order and sign th
MATH 340 FINAL EXAM
DECEMBER 17, 2009
1.(20) True or false. Give a brief reason.
a) If A is an m X 71 matrix with m < n then the system of equation
Ax = 0 always has a non-trivial solution. '
b) The determinant of any 11 X 11 matrix with A 2 At is zero.
(
$6. an
Final Exam
December 18, 2008 Math 340
Joel M. Cohen l 10:30 am- 12:30 pm
Name:
Put your nal answer to each problem in a unless problem calls for a proof.
Show all your work on these pages, using the backs for scratch paper. Check your
answers!
1. (
Math 340, Jerey Adams
Test I, October 11, 2010
For complete credit you must show all work
(1) [12 points] Compute:
(a) (1, 2, 3) (4, 5, 6)
(b) (1, 1, 1) (1, 0, 1)
(c) | 2v | if |v | = 5
(d) A unit vector n which is a multiple of (1, 2, 3)
(2) [20] Let v =
Math 340, Jerey Adams
Review, Chapter 7, December 3, 2010
1. Section 1
(a) Denition of iterated integrals
(b)
.
b
a
d(y )
c (y )
f (x, y ) dx dy ,
f (x)dx1 . . . dxn
2. Section 2
(a) Denition of Riemann integral
(b) For nice functions
(c) Computing
B
B
f
MATH 340 FINAL EXAM
DECEMBER 18, 2004
1.(10) Evaluate C F dr where F(x, y, z ) = (2xy, x2 + z 2 , 2yz + z ) and
C is the helix g (t) = (3 cos t, 3 sin t, 2t) for 0 t 2 .
2.(20) Let be the intersection of the ellipsoid 2x2 + y 2 + z 2 = 10 and
the elliptic
MATH 340 FINAL EXAM
DECEMBER 17, 2009
1.(20) True or false. Give a brief reason.
a) If A is an m n matrix with m < n then the system of equations
Ax = 0 always has a non-trivial solution.
b) The determinant of any 11 11 matrix with A = At is zero.
(At is
Math 340, Jerey Adams SOLUTIONS
Final Exam, December 15 , 2010
All Questions 20 points
Question 1 (a) The cross product is (1, 1, 2) (1, 2, 2) = (2 4, 2+2, 2 1) =
(2, 0, 1). The answer is all multiples of this.
(b) The determinant is c 1 + 3, which equals
[20]
[20]
' [20]
[20]
FINAL EXAM
Math 340 Fall 2012 Jakobson
Give some reason, justication or explanation for each of your answers. An-
swer each numbered question on a separate page.
1. (a) Convert parametric equations of two surfaCes into equations in