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Unformatted text preview: ' MATH 222 LEC 1 NAME: Instructor: Uhlenbro ck Please circle the discussion section that you are registered for: SOCIAL SCIENCE 5206 SOCIAL SCIENCE 5208 Disc 302: Addington, Nick Disc 303: Mantilla Soler, Guillermo
Disc 304: Addington, Nick Disc 307: Hunter, James Disc 305: Zheng, Fan Disc 308: Hunter, James Disc 306: Qi, Peng Disc 309: Mantilla Soler, Gillermo
Disc 310: . Qi, Peng Disc 312: Berliner, Adam Disc 311: Zheng, Fan
FINAL EXAM: WEDNESDAY DECEMBER 19, 2007
Do all problems and show all your work. Answers without written steps or reasons are worth much less than answers with correct steps. and reasons. Unless otherwise indicated
you should derive exact solutions to the problems; rather than numerical approximations. You can only get credit for what you write down, not for what you might have meant by ' a vague aIISWGI'. Write neatly and display your ﬁnal answers clearly. Use the last page for scrap paper. U'PROBLERJPOINTS—l SCORE—n MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM 1
( ’7 points ) Evaluate the following integral exactly fold: 111(33) dm Answer: ( 10 points ) Solve the initial value problem for y as a funetion of a: ' (z2+1)2% : w2+1, 31(0) : 1 MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM ' 2 ( 8 points ) Find the general solution, y as a function of :17, for the differential equation dy 37d eyhﬂ, where 95 >0.
:1: , { 11 points ) Find y as a function of as determined by the initial value problem . ——+y = 6: y(0)=0, y’(0)=3 MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM 3 ( ‘6 points ) Determine which kind of conic section is described by the equation 3x2 ~ 5xy+2y2—7x— 143/: —1 { 9 points ) Find 7‘ as a function of 0 for the conic section which has
eccentricity e = 1/5, one focus at the Origin, and corresponding directrix at y : —10. Answer: MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM 4 ( ’7 points ) Giving reasons, decide if the following series converges or diverges. 00
n
2 (In n)(”/2) n22 ( 10 points ) Find the complete Maclaurin series for the following function of m,
and write out the ﬁrst four terms explicitly (Hint: Use substitution.) mm) )
COS A V
 ( x/i ' MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM 5 ( 5 points ) Prove that the diagonals of a rhombus (i.e. a parallelogram, all of Whose
sides have equal length) are perpendicular. Consider the three points P(+2, 2, 0), Q(O, 1, —1) and R(*1, 2, —2).
( ’7 points ) Find a unit vector perpendicular to the plane through P, Q and R. ( 5 points ) Find the area of the triangle A PQR. Answer: MATH 222 LEC 1 FINAL EXAM WED DEC 19 PROBLEM 6 ( 8 points ) Find parametric equations (with parameter t) for the line through
P(2, 3, 0) which is perpendicular to both i+ 2j + 3k and Bi + 4j + 5k . Answer: ( 9 points ) Find the angle between the planes 550 + y — z = 10 and x + 2y — 3z : ——1 . ‘ ...
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 Fall '08
 Wilson
 Calculus, Geometry

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