Sample Exam 1 Answers
1. A car is being towed by a wire which exerts a force of 2000 pounds and makes an angle
of 30 from horizontal. Find the work done in moving the car 100 feet.
Solution: 100000 3 foot pounds
2. Find the volume of the parallelepiped sp
Math 114 - Fall 2016 - Assignment 6
Due: Friday, December 2nd at 4:30PM in dropbox 7 outside of MC 4066
Eigenvectors and Eigenvalues
4 0 0
1. Let A = 2 8 4 . Find the algebraic multiplicity, geometric multiplicity, and eigenspace of
4 5 0
each of the eige
Math 114 - Fall 2016 - Assignment 6 Bonus (5 marks)
Hand in with your Assignment 6.
The Earths rotation causes it to bulge out at the equator giving it the shape of an oblate ellipsoid.
The mass distribution of Earth is captured by its moment of inertia t
1
Math 114
Circle one:
FINAL EXAM
December 17, 2013
Professor Krishnan
Professor Shatz
Professor Yip
Professor Ziller
Name:
Penn Id#:
Signature:
TA:
Recitation Day and Time:
You need to show your work, even for multiple choice problems. A correct answer w
Dr. Zachary Scherr
1
Math 114
Exam 2 Practice
Curvature
1. The curvature of the helix r(t) = 4 sin 2t, 4 cos 2t, 6t is constant. Find this curvature.
2. Consider the ellipse r(t) = a cos t + b sin t. Find the values of t for which the curvature is largest
Dr. Zachary Scherr
1
Math 114
Exam 3 Practice
Double Integrals
1. Evaluate
0
x
sin(y)
dydx.
y
(Hint: Change the order of integration).
2. Write an equivalent integral with the order of integration reversed
tan1 y
3
xydxdy.
0
0
3. Find the area of the port
Dr. Zachary Scherr
1
Math 114
Exam 2 Practice
Curvature
1. The curvature of the helix r(t) = 4 sin 2t, 4 cos 2t, 6t is constant. Find this curvature.
Solution:
4
25
2. Consider the parabola y = 3x2 . Find the curvature at x = 0 (Hint: we can parametrize t
Dr. Zachary Scherr
1
Math 114
Exam 3 Practice Answers
Double Integrals
1. Evaluate
x
0
sin(y)
dydx.
y
(Hint: Change the order of integration).
Solution:
2
2. Write an equivalent integral with the order of integration reversed
tan1 y
3
xydxdy.
0
0
Solution
Math 114 Practice Problems for Test 3
Comments:
0. Surface integrals, Stokes Theorem and Gauss Theorem used to be in the Math240
syllabus until last year, so we will look at some of the questions from those old exams
for practice. Some of these will be ch
Sample Exam 1 Problems
1. A car is being towed by a wire which exerts a force of 2000 pounds and makes an angle
of 30 from horizontal. Find the work done in moving the car 100 feet.
2. Find the volume of the parallelepiped spanned by
v1 = 2 + k
v2 = + 2 +