166E1-S06 - MA 166 EXAM 1 Spring 2006 Page 1/4 NAME...

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Unformatted text preview: MA 166 EXAM 1 Spring 2006 Page 1/4 NAME 10—DIGIT PUID RECITATION INSTRUCTOR RECITATION TIME 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 or calculators may be used on this test. (10) 1. Let 6', 5, 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. (05545 T (11)&'><5=5><d T (m)a (Exa:(d-b)x(a 6') T (1v) 5 (5+E’)=d 5+6 5 T (v)((_1'><_‘)><&'=6 T (7) 2. Find the center and radius of the sphere a32+y2+z2—2:r+6z=15 MA 166 Exam 1 Spring 2006 Name Page 2/4 —» (15) 3. If a: 7+ 23"— ka nd 5 = 33+ 13, find the following ) 13' (a 91 II (c) cos0 where 0 is the angle between 61' and I; (d) the area of the parallelogram determined by C73 and I; (e) a unit vector orthogonal to both 61' and I: (6) 4. Let A(1, 2) and B(2, 0) be two points in the plane. Find the coordinates (p, q) of the point C(p, q) such that AC’ —— 2AB. (8) 5. Find the value of the number c such that the vectors (1, c, 2) and( 2, —1,—4) are (a) orthogonal _ c : (b) parallel MA 166 Exam 1 Spring 2006 Name _— Page 3/4 (10) 6. Find thearea of the region enclosed by the curves 31:31:2 and y=x+2. (16) 7. Set up, but do not evaluate, an integral for the volume V of the solid obtained by rotating the region bounded by the curves y = :34, y : 0, and :1: = 1, about the x—axis, (a) using the method of disks / washers <. H \ (b) using the method of cylindrical shells < H \ MA 166 Exam 1 Spring 2006 Name ____— Page 4/4 8 8. Using the method of disks washers, set u , but do not evaluate, an integral for the P volume V of the solid obtained by rotating the region bounded by the curves 3/ = 0, y = sinx, 0 g a: 3 7r about the line 3/ : 1. (8) 9. A force of 10 1b. is required to hold a spring stretched 4 in. beyond its natural length. How much~work is done in stretching it from its natural length to 6 in. beyond its natural length? ft—lb (12) 10. Find /(1n:1:)2d$. ...
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