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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.
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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.
(a) 4x-2y+6z= (b) -6x+3y-9z=- (c) 4x-2y-2z= (d) z=2x-y-
t, t^2 , t^3
at the point (1, 1 , 1).
x, and x = 0. ∫ ∫
D
sin(2 + y^4 )dA
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.