MATH 23 – Final Exam Fall Semester 2008, Exams of Calculus

The final exam for math 23 during the fall semester of 2008. The exam consists of 9 problems, each with a different score. Students are required to answer all questions without the use of books or calculators, but they may use a half sheet of paper. The total number of points is 100.

Typology: Exams

2012/2013

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MATH 23 Final Exam Fall Semester 2008
Duration: 180 minutes
Instructions: Answer all questions, without the use of books or calculators. You may have a half
sheet of 8.5X11 paper with both sides filled out. Partial credit will be awarded for correct work.
You may use the back of the pages of the exam should it be necessary, but please indicate in writ-
ing that you have done so. The total number of points is 100. Please write at the top of the exam
“drop” or “replace”, depending on how you wish your second midterm grade to be computed.
The problems with a “*” are those that will count toward your second midterm score should you
choose the “replace” option.
Problem Score
1
2
3
4
5
6
7
8
9
Total
1
pf3
pf4
pf5

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Duration: 180 minutes Instructions: Answer all questions, without the use of books or calculators. You may have a half sheet of 8.5X11 paper with both sides filled out. Partial credit will be awarded for correct work. You may use the back of the pages of the exam should it be necessary, but please indicate in writ- ing that you have done so. The total number of points is 100. Please write at the top of the exam “drop” or “replace”, depending on how you wish your second midterm grade to be computed. The problems with a “*” are those that will count toward your second midterm score should you choose the “replace” option.

Problem Score

Total

  1. (10 points) Which of the following four planes are parallel? Are any of them identical?

(a) 4x-2y+6z= (b) -6x+3y-9z=- (c) 4x-2y-2z= (d) z=2x-y-

  1. (10 points) Find the parametric equations for the tangent line of the curve r(t) =

t, t^2 , t^3

at the point (1, 1 , 1).

  1. (10 points*) Compute the following double integral where D is the region bounded by the curves y = 2, y = 3

x, and x = 0. ∫ ∫

D

sin(2 + y^4 )dA

  1. (10 points) Let F be the two dimensional vector field given by F(x, y) =

x^3 , sin y

. Let the curve C be the part of the ellipse x^2 + y^2 4

= 1 in the upper half plane and oriented counterclockwise. Find the line integral

C F^ ·^ dr.

  1. (15 points) Let W be the cylinder with radius 1 and height 4 placed in a coordinate space so that its center coincides with the z-axis and its base lies on the xy-plane. Suppose further that the density of the cylinder is given by ρ(x, y, z) = (1 + z) sin(x^2 + y^2 ). Find the center of mass of the cylinder.