166E1-S08 - 4 5 6 (10) 1. (4) 2. (4) 3 MA 166 EXAM 1 Spring...

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Unformatted text preview: 4 5 6 (10) 1. (4) 2. (4) 3 MA 166 EXAM 1 Spring 2008 Page 1 / 4 NAME ‘ Page 1 / 18 10—DIGIT PUID Page 2 /24 RECITATION INSTRUCTOR Page 3 /28 Page 4 / 30 RECITATION TIME TOTAL /100 DIRECTIONS 1. . Find Ei- gif Idl = 12, = 15 and the angle between 5 and his 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. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. . 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. . Credit for each problem is given in parentheses in the left hand margin. . No books, notes or calculators may be used on this test. Let (i, 3, E be three—dimensional vectors. For each statement below, circle T if the statement is always true, or F if it is not always true. (i) (an-(313') =6d-5’ (ii) (5.1%: (13’ .35 (iii) (a— 13') . (5+ 13') = m2 — |z7|2 (iv) ax(5xa)=(ax6)xa HHHHH ’fi'fl'ij’ij'fi (v) If (i X 3:.‘5 then 6 and I; are parallel If 5 = 2;- 5+ 21;, find a unit vector in the direction opposite to E. S 71' . E radlans. MA 166 Exam 1 Spring 2008 Name _— Page 2/4 (6) 4. Find the values of t for which the vectors (3t, ——t, —3) and (—-1,t2, —4t) are orthogonal. t = (4) 5. A constant force F" 2 317+ 55+ 10]; moves an object along the line segment from (1,0, 2) to (5, 3, 8). Find the work done if the distance is measured in meters and the force in newtons. W: J (6) 6. Find the area of the parallelogram determined by the vectors (i 2 5+ 5j+ I; and b = ~2§+ 3' + 3k. $2+y2+z2+2x—10y=—1. (8) 7. Find the center and radius of the sphere MA 166 Exam 1 Spring 2008 Name _— Page 3/4 (10) 8. The region bounded by the curves :1: = y2 + 1, y = —1, y = 1, and a: = 0 is rotated about the y—axis. Find the volume of the resulting solid. S (10) 9. Find the volume of the following solid 5' : The base of S is a circular disk with radius 7". Parallel cross—sections perpendicular to the base are squares. (8) 10. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curves at = x/siny with 0 g y 3 7r, and a: = 0, about the line y = 4. MA 166 Exam 1 Spring 2008 Name —__ Page 4/4 (8) 11. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curves y = m2 + 1, y = 9 — :32 about the line y = —1. | (6) 12. The natural length of a springis 1m and a force of lON is required to hold the spring stretched to a total length of 2m. How much work is done in stretching the spring from its natural length to a length of 1.5m? (16) 13. Evaluate the integrals. (a) ftan‘1 mdx ...
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166E1-S08 - 4 5 6 (10) 1. (4) 2. (4) 3 MA 166 EXAM 1 Spring...

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