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
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
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 distr
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
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.
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 rev
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 .
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 orde
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
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