The material included here does not necessarily reﬂect what will be on the actual exam. Make sure to go over the review problems Professor Frenkel posted on his webpage. I recommend ﬁrst looking over all the problems and deciding which strategy to use, before actually calculating anything. (1) Let S be the part of the plane 2x + 3y + 4z = 12 that lies in the ﬁrst octant, with upward orientation. Compute the surface integral S F · dS, where F = xi + yj + zk. (2) Let F be the vector ﬁeld x2 + y 2 , xy + z, z 2 and C be the curve of intersection of the sphere x2 + y 2 + z 2 = 4 and the plane x = 1, oriented counterclockwise when viewed from the positive xaxis. Compute C F · dr. (3) Let S be the surface consisting of the two spheres x2 + y 2 + z 2 = 1 (oriented inward) and 2 x2 + y 2 + z 2 = 4 (oriented outward), and let F = e2yz i + yzj − sin(x2 y)k. ﬁnd S F · dS. (4) Find the mass of the cylindrical region x2 + z 2 = 1, 0 ≤ y ≤ 3, if its density is given by √ ρ(x, y, z) = y x2 + z 2 . (5) Mark each of the following as True or False y x (a) If F = 2 i− 2 j, then F · dr = F · dr, where C1 is the straightline x + y2 x + y2 C1 C2 path from (−1, −1) to (1, −1) to (1, 1), and C2 is the straightline path from (−1, −1) to (−1, 1) to (1, 1). (b) If S is the hemisphere x2 + y 2 + z 2 = 1 with y ≥ 0, oriented towards the positive yaxis, and C is the curve parametrized by cos t, 0 sin t , 0 ≤ t ≤ 2π, then Curl F · dS = S C
F · dr
for any F whose components have continuous partial derivatives on R3 . (c) A vector ﬁeld P i + Qj + Rk on R3 is conservative if there is a function f (x, y, z) such that ∂f = P , ∂f = Q, and ∂f = R. ∂x ∂y ∂z 3 (d) There is a vector ﬁeld F on R3 such that Curl F = 2x2 y + 3z, xy 2 − 3yz, 2 z 2 − 5xyz .
(e)
x2 y dx + xy 2 dy = C2 x2 y dx + xy 2 dy, where C1 , C2 are circles in R2 of radius one and two, respectively, both centered at (0, 0) and oriented counterclockwise. C1
...de Contaduría Pública y Administración
International Business Program

Instructional Guide for the Final Project 
The Managerial Process 

Professor: Lic. Ana Esperanza Álvarez García 
January  June 2013 
Final Assignment
The Final Assignment is an integrated business where, the first semester final assignment will serve as a base for making this semester final assignment.
I. General...
...material, which may have made the final result boring had I left it like this.
3. Final Sketch:
After we completed our experiments with materials, I came up with a more developed concept and sketch. I used the same basic concept, but I added a city on the bank. I also put pieces that I thought described my life in the river this time. I decided to try and use powder paste for the river, and gouache for the background. This...
...This pack of BUS 600 Week 6 Final Paper includes:
Social Networking with WalMart
Business  General Business
Final Paper
The final assignment for this course is a Final Paper. The purpose of the Final Paper is for you to culminate the learning achieved in the course by completing a final research project on organizational communication processes. The Final Project represents...
...EVALUATION
The theme for my final GCSE Art and Design assignment was ‘Ordinary and/or Extraordinary’. I was given the exam paper just prior to going on a family holiday to the desert in Southern California and I decided that as Borrego Springs (the place that we visited) is such an unusual and extraordinary place, I would use it as my starting point in developing my ideas and investigations based on the theme. Borrego Springs provided me with both an intriguing place to...
...ADVANCED SPEECH
FINAL SPEECH EVALUATION
NAME______________________________
TOPIC_________________________________________
TYPE OF SPEECH________________________________
5 4 3 2 1
Rate the speaker on each point: Excellent Good Average Fair Poor
INTRODUCTION
Gained attention and interest 5 4 3 2 1
Clear transition sentence 5 4 3 2 1
Previewed body of...
...MBA 610: Final Paper Description and Grading Guide
Overview
In a wellcrafted, comprehensive paper, use specific cases, statutes, course resources, and course concepts to demonstrate your competency with regard to all of the following three points:
1. Areas of the law that you feel most affect business decisions (Law and Business Decisions)
2. Major underlying principles of the law that you feel are most impactful (Impactful Law Principles)
3. Common sources of fear and...
... served in the Royal Air Force from the start of World War II in 1939 until 1947, Soon he went to live in Canada. Most of his novels were written in the period between 1960s and 1990s. These are Flight into Danger, "Hotel," "Wheels," The Final Diagnosis. Hailey was best known for writing "Airport. Several of them were made into TV shows and films. "Airport" was adapted to the big screen in 1970 and helped launch the disaster movie genre. Airport became a blockbuster...
...INT 610: Group Project Guidelines and Grading Guide
Overview
The final project for this course is a written International Investment Report and a Summary Presentation. Your company wants you and your colleagues to research a possible investment in a foreign country. Your team will be given an industry and a country. You will need to pick a company in the industry. This can be an existing real company (Eg. Starbucks) or a fictitious company made up by your team.
You must...