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 become detached, write your name on them and point them
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. (5 points) Find the curl and divergence of the vector
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 function f such that F =
F dr, where
C
f and evaluate
F
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 become detached, write your name on them and point them
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
x2 + y 2 = 4.
Problem 2. (5 points) Find the center of m
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 integration and change the order
of integration.
1
4
f (x, y) dy
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) Find the maximum and minimum values of the function
f (x
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 do become detached, write your name on them and point th
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(t2 ) j + t cos t k
t+1
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 become detached, write your name on them and point them
ou
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 the line r = (i + j + k) + t(i j + k).
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 surface integral
xyz dS
S
where S is the part of the co
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 line integral along the curve.
(2x y) dx + (x + 3y) dy
C
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 do become detached, write your name on them and point t
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).
Problem 2. (5 points) Integrate f (x, y) = ex
the semicircl
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) Evaluate.
9x2
3
9x2 y 2
x2 + y 2 dz dy dx
3
0
0
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 points) Calculate the iterated integral.
2
1
(4x3 9x2 y 2
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 the Chain Rule to nd
z = tan1 (y/x),
x = et ,
dz
.
dt
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 implicitly by
x2 + y 2 + z 2 6x + 8y 24z = 0
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 become detached, write your name on them and point the
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 t 2
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 a vector that has the same direction as 1, 2, 3
but ha