MTH 222
Final
December 19, 2011
Name:
This test consists of 10 problems on 11 pages (including this cover sheet).
The exam is worth 200 points. Do not separate the pages of this exam. If
any pages do
Quiz
19APR10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Use Greens Teorem to evaluate the line integral
2
(2y + ex ) dx + (3x + arctan y) dy
C
where C is the circle x2 + y 2 = 25
Problem 2
Quiz
12APR10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Evaluate the line integral
C
F dr, where
F(x, y, z) = z i + x j + y k,
r(t) = t i + t2 j + t3 k, 0 t 1
Problem 2. (5 points) Find a
MTH 222
Midterm #2
March 26, 2010
Name:
This test consists of 5 problems on 6 pages (including this cover sheet). The
exam is worth 100 points. Do not separate the pages of this exam. If any
pages do
Quiz
22MAR10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Evaluate the integral R (x + y) dA, where R is the
region that lies to the left of the y-axis between the circles x2 + y 2 = 1 and
x
Quiz
15MAR10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Calculate the double integral.
cos(x + 2y) dA,
R
R = cfw_(x, y) | 0 x , 0 y /2
Problem 2. (5 points) Sketch the region of integratio
Quiz
8MAR10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the rate of change and direction of fastest increase of
f (x, y, z) = x3 y 2 z 2
at the point (1, 2, 3).
Problem 2. (5 points) F
Quiz
15FEB10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find and sketch the domain of the function
f (x, y) =
y+
25 x2 y 2
Problem 2. (5 points) Find the limit
lim
(x,y)(0,0)
xy
x2 + y 2
MTH 222
Midterm #1
February 3, 2010
Name:
This test consists of 5 problems on 6 pages (including this cover sheet). The
exam is worth 100 points. Do not separate the pages of this exam. If any
pages d
Quiz
1FEB10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the limit.
lim
t0
sin t t + 1 3
,
,t
t t2 1
Problem 2. (5 points) Find the derivative of the vector function.
r(t) =
et
i + sin(
Quiz
25JAN10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find a unit vector that makes an angle of 60 with
3, 4 .
Problem 2. (5 points) Compute (i + j + k) (i + 3j + 2k).
MTH 222
Final
April 28, 2010
Name:
This test consists of 12 problems on 12 pages (including this cover sheet).
The exam is worth 200 points. Do not separate the pages of this exam. If
any pages do bec
Mth 222-01 Quiz
15 Sep 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find |a 3b| if a = 2i 3j + k and b = i + j + k.
Problem 2. (5 points) Find 1, 2, 3 1, 1, 7 .
Mth 222-01 Quiz
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find 1, 2, 3 1, 1, 7 .
22 Sep 2011
Problem 2. (5 points) Find an equation for the plane through the point
(1, 2, 3) orthogonal to
Mth 222-01 Quiz
8 Dec 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the curl and divergence of the vector eld.
F(x, y, z) = xy i + x2 z j + xyz k
Problem 2. (5 points) Evaluate the
Mth 222-01 Quiz
1 Dec 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Evaluate
2xy 3 dx + 3x2 y 2 dy
C
along, C, the arc y = ex from (0, 1) to (1, e).
Problem 2. (5 points) Evaluate the li
MTH 222
Midterm #2
November 17, 2011
Name:
This test consists of 6 problems on 7 pages (including this cover sheet). The
exam is worth 100 points. Do not separate the pages of this exam. If any
pages
Mth 222-01 Quiz
3 Nov 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Evaluate the double integral.
x2 y dA
D
where D is the triangular region with vertices (0, 0), (3, 0) and (3, 6).
Prob
Mth 222-01 Quiz
10 Nov 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the area of the part of the plane 2x+5y +z = 10
that lies inside the cylinder x2 + y 2 = 9.
Problem 2. (5 points
Mth 222-01 Quiz
27 Oct 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the local maxima, local minima and saddle
points of the function
f (x, y) = x3 y 3 3x + 3y + 4
Problem 2. (5 poi
Mth 222-01 Quiz
20 Oct 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find an equation of the tangent plane to the surface
z = x ln(x 2y) at the point (3, 1, 0).
Problem 2. (5 points) Use
Mth 222-01 Quiz
13 Oct 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find the limit.
x4 y 4
(x,y)(0,0) x2 + y 2
lim
Problem 2. (5 points) Find
z
x
and
z
y
if z = f (x, y) is dened implic
MTH 222
Midterm #1
October 3, 2011
Name:
This test consists of 6 problems on 7 pages (including this cover sheet). The
exam is worth 100 points. Do not separate the pages of this exam. If any
pages do
Mth 222-01 Quiz
29 Sep 2011
Name:
(This quiz has two sides.)
Problem 1. (5 points) Find T(t).
r(t) = cos 5t, sin 5t, 12t
Problem 2. (5 points) Find the length of the curve.
r(t) = cos 3t, sin 3t, 4t
0
Quiz
20JAN10
Name:
(This quiz has two sides.)
Problem 1. (5 points) Show the equation
x2 + y 2 + z 2 + 8x 6y + 2z + 17 = 0
represents a sphere, and nd its center and radius.
Problem 2. (5 points) Find