166E1-S09 - MA 166 Exam 1 Spring 2009 Page 1/4 NAME Page 1...

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Unformatted text preview: MA 166 Exam 1 Spring 2009 Page 1/4 NAME Page 1 / 16 10—DIGIT PUID Page 2 /25 RECITATION INSTRUCTOR Page 3 m Page 4 / 33 RECITATION TIME r———— TOTAL /100 DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators, or any electronic devices may be used on this test. 1. Let 6, 5, 5' be three—dimensional vectors. For each statement below, circle T if the statement is always true, or F if it is not always true. (10) (i) If 65 and 1:): are unit vectors and 0 is the angle between them, then 6- b = c056 (ii) IfZ-Ezi-E, thenl7=6 (iii) If 5-13: 0, then (5+ 1312 = |Ei|2 + (5F (iv) The vector 6 x X E) is always parallel to I; X E w)wxaxa=6 H H H H a w w m w m (6) 2. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3)- MA 166 Exam 1 Spring 2009 Name —_____ Page 2/4 (4) 3. Find the values of c for which the vectors (0,2, 3) and (2, c, ~2) are orthogonal. (4) 4. If 17:: (1,2, 2) and 'u')’ = (1,0,1), find the angle 6 between 17 and 122’. Q (4) 5. A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of 30° above the horizontal moves the sled 80 ft. Find the work done by the force. (13) 6. Consider the points P(1,—2,1),Q(—1,3,2) and R(2,1,1). (a) Find 132) x 132%. (b) Find the area of the triangle with vertices P, Q, R. (c) Find two unit vectors orthogonal to the plane through the points P, Q, and R. MA 166 Exam 1 Spring 2009 Name —___ Page 3/4 (10) 7. Find the area of the region in the first quadrant bounded by the curves y = 3:3 and 2 y = a: + 2x. (8) 8. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating about the y—axis, the region bounded by the curves x=siny, Ogygw, andm=0. (8) 9. Let R be the region bounded by the curves y = 2: ~ 3, y : 0, and x = 0. Use the method of disks or washers to set up an integral for the volume of the solid obtained by rotating R about the line 3/ = 2. Do not evaluate the integral. MA 166 Exam 1 Spring 2009 Name —_——, Page 4/4 (8) 10. Let R be the region bounded by the curves y z x2 and y : 2 — 362. Use the method of cylindrical shells to set up an integral for the volume of the solid obtained by rotating R about the line a: = 1. Do not evaluate the integral. (8) 11. If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lbs, how much work is needed to stretch it 9 in beyond its natural length? (7) 12. /x3ln3:dzv= (10) 13. First make a substitution and then use integration by parts to evaluate the integral / cos x/E dzc. ...
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166E1-S09 - MA 166 Exam 1 Spring 2009 Page 1/4 NAME Page 1...

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