MATH 241H Exam 1 (February 17, 2012)
Please answer each numbered question on a dierent answer sheet. Make sure your name, my
name, and the appropriate problem number appear on each answer sheet. You only need to sign
the pledge on the rst answer sheet. Sh
MATH 241H - EXAM 3 - Dec. 11, 2002
(20) 1. Evaluate
C
y 2 dx + (x + sin(y 2 ) dy where C is the path pictured below which
travels from (1, 0) to (1, 0) along the x-axis, and then travels back to (1, 0) along the top
half of the circle x2 + y 2 = 1.
(20) 2
MATH 241H - EXAM 1 - February 12, 2007
[10] 1. Find symmetric equations for the line containing the points (1, 1, 4) and (3, 2, 4).
[10] 2. Find an equation of the plane that contains the point (2, 1, 1) and is perpendicular
to the line with parametric eq
MATH 241H - EXAM 2 - March 12, 2007
No Calculators - Show your work.
[20] 1. Let
y3
f (x, y ) =
x2 +y 2
0
if (x, y ) = (0, 0)
if (x, y ) = (0, 0).
(a) Find lim(x,y)(2,1) f (x, y ) or explain why it doesnt exist.
(b) Find lim(x,y)(0,0) f (x, y ) or explain
MATH 241H - EXAM 3 - April 16, 2007
No calculators. Show your work.
[15] 1. Evaluate the integral. (Hint: change to polar coordinates)
2
4x2
x2 + y 2 dydx
2
0
[20] 2. Find the surface area of the surface parametrized by
r(u, v ) = (u2 + v ) i + (u2 v ) j
MATH 241H - EXAM 1 , September 29, 2003 - Solutions
1. (a) a b
(b) (a b/a a) a
(c) ( a / b ) b
2. The plane is given by (3, 2, 0) + s(2, 1, 1) + t(1, 1, 3) so P0 = (3, 2, 0) is a point and a = (2, 1, 1) and b = (1, 1, 3) are vectors in the plane. To get a
MATH 241H - EXAM 1 , September 29, 2003
No Calculators - Show your work.
(15) 1. Let a and b be non-zero vectors in R3 . Use dot and cross products to give
expressions for vectors satisfying the following geometric conditions.
(a) A vector orthogonal to b
MATH 241H - EXAM 2 , October 27, 2003
No Calculators - Show your work.
(21) 1. Let x(t) = (cos t, sin t, 3t), 0 t 2 .
(a) Find the length of the path x.
(b) Find parametric equations for the line tangent to the path x when t = /2.
(c) Find the curvature f
MATH 241H - EXAM 3 - November 24, 2003
No calculators. Show your work.
[20] 1. Evaluate the integral
W
x2 + y 2 dV where W is the solid region bounded by
the paraboloids z = 1 + x2 + y 2 and z = 9 x2 y 2 .
In problems 2,3,and 4, evaluate the work integral
MATH 241H - Final Exam - December 15, 2003
Show your work. No calculators.
2
[40] 1. A curve is parametrized by x(t) = t2 i + 3 (2t + 1)3/2 j + 3 k, 0 t 2.
(a) Find parametric equations for the line tangent to the curve at the point x(1).
(b) Evaluate x x
MATH 241H - EXAM 3 - November 24, 2003 - Solutions
No calculators. Show your work.
1. The paraboloids intersect when 9 r2 = 1 + r2 so that r = 2. Thus
2
2
x2
+
y2
9r 2
r2 dz dr d = 256/15.
dV =
0
W
1+r 2
0
2. Use Greens Theorem with Nx My = x2 + y 2 and D
MATH 241H Exam 2 (Wednesday, March 14, 2012)
Please answer each numbered question on a dierent answer sheet. Make sure
your name, my name, and the appropriate problem number appear on each answer
sheet. You only need to sign the pledge on the rst answer s
Name:
Please answer each question in the space provided using the back if necessary. Show all work and
be sure your answers are complete, with explanations where necessary.
1. (4 pts) Find a unit vector in the direction of 3i 6j + 2k.
|3i 6j + 2k| = 9 + 3
MATH 241H: Quiz 2 (Monday, February 6, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show
all work and be sure your answers are complete, with explanations where necessary.
1. (7 pts) Find the equation of the l
MATH 241H: Quiz 3 (Monday, February 13, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show all work and
be sure your answers are complete, with explanations where necessary.
1. Consider the lines given by the s
MATH 241H: Quiz 4 (Monday, February 27, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show all work and
be sure your answers are complete, with explanations where necessary.
1. Determine if each of the followin
MATH 241H: Quiz 5 (Monday, March 5, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show
all work and be sure your answers are complete, with explanations where necessary.
1. Let f (x, y ) = xexy + y
dy
(a) (5 pt
MATH 241H: Quiz 6 (Wednesday, March 28, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show
all work and be sure your answers are complete, with explanations where necessary.
1. Find
R
ydA where R is the region
MATH 241H: Quiz 7 (Monday, April 2, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show all work and
be sure your answers are complete, with explanations where necessary.
1. Calculate the surface area of the Sph
MATH 241H: Quiz 8 (Monday, April 9, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show
all work and be sure your answers are complete, with explanations where necessary.
Suppose a silo of corn is bounded by the
MATH 241H: Quiz 9 (Monday, April 16, 2012)
Name:
Please answer each question in the space provided using the back if necessary. Show
all work and be sure your answers are complete, with explanations where necessary.
Suppose a sh bowl is made by taking the
Math 241H Section 0101 Spring 2012 Syllabus
Instructor: Beth Wilson
email: bethmcl@math.umd.edu
Oce: MATH 0206
www.math.umd.edu/bethmcl/
Math241.html
General
Information
This course will meet every Wednesday and Friday from 12:00-12:50pm in Math
0302, an