Fall 2007 Calc 3- Exam 1

Fall 2007 Calc 3- Exam 1 - MA 261 Name Student ID EXAM 1...

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Unformatted text preview: MA 261 Name Student ID EXAM 1 Fall 2007 Recitation Instructor Recitation Time Directions 1. Write your name, student ID number, recitation instructor’s name and recitation time in the spaces provided above. . Write your name, your student ID number and division and section number of your recitation section on your answer sheet, and fill in the corresponding circles. . Mark the letter of your answer for each question on the answer sheet as well as in the test papers. . The exam has 12 problems. Problem 1~8 are worth 8 points and problem 9—12 are worth 9 points each. . N 0 books, notes or calculators may be used in this exam. CL QQC/g Agaic 1. The projection of the vector V = i — 3j + 4k onto the vector b = i +j is A. projbvz —i—j 1 B. ro' v=—i+' p Jb fi( J) . 1. . C. pIOJbV=§(1+_}) D ro' v——L(i—') ' p .]b W J . 1 . E. pI‘OJbV: §(1—_]) 2. The area of the triangle with vertices at (a, 0, 0), (0, 2a, 0) and (0, 0, 3a) is 3&2 A A:— 2 B. A=5a2 7a2 C A"; D A=6a3 3 E Azgi 2 3. The graph of the surface 3:2 — yZ + £2 9 = —1 looks most like : B 4. A line L contains the point (1, 2, —1) and is perpendicular to the plane 33: + y — 52 = 1. What point on L intersects the plane y = 0? A. (9, 0, —5) B. (—9, O, 5) C. (5, 0, —9) D. (~5, 0,9) E. There is no point of intersection 5. Find spherical coordinates (,0, (9, <75) for the point P whose rectangular coordinates are ( 1 fl, 1 fl: 21> PU .0 “N 00 PM: 001:1 Mile cola A>l>1 CM: ms Na Na DJ|=I V \_/ \_/ V \_/ O /‘\/—\/-\A H /—\ UN 6. The unit tangent vector to the curve r(t) 2 (cost, sin 3t, €t> at the point (1,0,1) is: 7. Find the length of the curve r(t) epcwe 3 1 07—,— < 10 10> 1 1 07—)— < 2 2> ~1—1 13,—,— < \/§\/§> —1 1 Oa—aoafi < fl fi> — 3 1 <W’U’W 2 4 6 8 10 8 . Evaluate lim x2e‘y (mm—42,0) A. —4 B. 4 C. 0 D. 6‘4 E. does not exist 9. Find the domain of {I} f($,y)=1n(y+2> A. y7é—2, x>0 B. y>—2,x>00ry<—2,x<0 C. y>—2,:E>0 D. y>0,a:>0 E. y>0, $>00ry<—2, x<0 10. Compute the tangent plane of the surface 2 = 2533/2 — E at (2, 1, 2) y A. z=x—5y+5 B. 2:56—63/ C. z=x+5y—5 D. z=2x+y—3 E. z=m+10y~10 11. Hz 2 :L'2+y4 and x = —211 and y = u—v, compute % at (u,v) = (2,1). A. —4 B. —12 C. O D. 4 E. 12 12. Find the rate of change of the function f($, y) = 2x + 3y at the point (1, 2) in the direction of the vector v = 3i + j. e .U .o .w .> gt “9 Elm 8'0 51w ...
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Fall 2007 Calc 3- Exam 1 - MA 261 Name Student ID EXAM 1...

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