Name:_
MATH 211-001 - Multivariable Calculus
February 24 2012
TEST n.1
Instructions: Show all work needed to obtain your answers.
Please note: you are expected to obey the Honor Code when taking this test.
Exercise 1. (20pts) Given the three points P (1,
Math 221: Linear Algebra
Homework assignment 4
Dr. M. H. Mertens
Exercise 1.
Show that R2 cannot be spanned by one vector.
v1
v2
Solution. We look at the span of an arbitrary vector v =
R2 . There are two cases to
distinguish:
1
R2 is certainly not in v
Trigonometry Review
Math 211 - Trig Review - Prof. Louie
First, starting with the very basics, we should all know SOHCAHTOA.
sin x =
opposite
hypotenuse
csc x =
1
sin x
cos x =
adjacent
hypotenuse
sec x =
1
cos x
tan x =
opposite
adjacent
cot x =
We shoul
Name:_
MATH 211-001, Multivariable Calculus
April 6th 2012
quiz n.8
Exercise 1. Sketch the region of integration and change the order of integration:
ln x
2
f (x, y ) dy dx
1
0
1
Exercise 2. Use polar coordinates to compute the integral
2 y2
1
(x + y ) dx
Name:_
MATH 211-001, Multivariable Calculus
Mar 30 2012
quiz n.7
Exercise 1. Find the rst- and second- order degree Taylor polynomials L and Q of f (x, y ) = ex
(0, 0).
1
2
y2
at
Exercise 2. Consider the vector eld F (x, y ) = 2x e y i + (2 y x2e y) j .
Name:_
MATH 211-001, Multivariable Calculus
Mar 23 2012
quiz n.6
Exercise 1. If u = x2 y 3 + z 4, where x = p + 3 p2, y = pe p, and z = p sin p, use the Chain Rule to nd
du/dp.
1
Exercise 2. Consider the function f (x, y ) = 3x2 y 2 + 2x.
i. Find the maxi
Name:_
MATH 211-001, Multivariable Calculus
Mar 2 2012
quiz n.5
Exercise 1. Describe the level surfaces of the function f (x, y, z ) = x2 y 2 z 2. Where are they dened?
How do they look like? [Hint: use cross sections to study how the surfaces change as f
Name:_
MATH 211-001, Multivariable Calculus
Feb 17 2012
quiz n.4
Exercise 1. A guitar string is stretched tight along the x-axis from x = 0 to x = L. Each point on the
string has an x-value, 0 x L. As the string vibrates, each point on the string moves ba
Name:_
MATH 211-001, Multivariable Calculus
Feb 10 2012
quiz n.3
Exercise 1. Using a parameterization, nd
C
F dr for the given F and C :
F = xi + yj + zk and C is the path consisting of a line from (2, 3, 0) to (4, 5, 0), followed by a line
from (4, 5, 0)
Name:_
MATH 211-001, Multivariable Calculus
Feb 3 2012
quiz n.2
Exercise 1. Write the formula for a vector eld in 2-space such that all vectors are parallel to the y -axis
and all vectors on a horizontal line have the same magnitude. Sketch the vector eld
Name:_
MATH 211-001, Multivariable Calculus
Jan 27 2012
quiz n.1
Exercise 1. Given the force vector F = 2i and the displacement d = i + j ,
a) nd the parallel and perpendicular components of F in the direction of d ;
b) nd the work W done by F through the
Math 221: Linear Algebra
Homework assignment 5
Dr. M. H. Mertens
Exercise 1.
For the following matrices, compute all dened products of two matrices.
1 1 1
2 0 0
A := 2 0 1 R33 , B := 1 1 0 R33
0 0 1
3 0 2
2
0 2 0 0
C := 1 1 1 0 R34 , D := 1 R31
3
0 3 0