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162E1-S2005

# 162E1-S2005 - MA 162 Exam 1 Spring 2005 Name Student ID...

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Unformatted text preview: MA 162 Exam 1 Spring 2005 Name: Student ID: Lecturer: Recitation Instructor: Recitation Time: Instructions: 1. This package contains 12 problems worth 8 points each. 2. Please supply a_ll information requested above and on the mark—sense sheet. 3. Work only in the space provided, or on the backside of the pages. Mark your answers clearly on the scantron. Also circle your choice for each problem in this booklet. 4. No books, notes, or calculator, please. MA 162 Exam 1 Spring 2005 1. A unit vector in the same direction as the vector 4i — 2j + 4k is 2. Which of the following statements are true? (a and b are vectors in space). I. If a and b are orthogonal then a - b = 0. II. If a and b are orthogonal then a x b = 0. III. a x b is orthogonalio—a and b. A. 2i—j+2k. B. gi — %j + gk. C. %i + §j — ék. D. 3i — %j + 3k. E. —-:;i + gj + 2k. A. onlyI B. only 111 C. only I and III D. only I and II E. all are true 3. The area of the parallelogram determined by the vectors (1, —2, 1) and (1, 2,0) is A. 21 B. \/2_1 C. 18 D. V18 E. 6 4. The area of the region enclosed by the curve y = e” and the lines y = —1 — a3, :1; = —1 and a: = 0 is 1 e 5. The region enclosed by the curve 3/ = sinx (0 g x 3 7r) and the 1: axis is rotated about the line y = —1. The volume of the solid thus generated is A. 27r/ (sin2x— 1)2 d3: 0 71' B. «/ (1+sin2x)da: o C. 27r/ m(1+sin:c)dx 0 D. 27r/ x(1+sinm)2dac o E. 7r/1r {(1 +sinw)2 — 1} dm 6. If the region under the curve 3/ = 3x4 and above the :1: axis, —2 S :1: S 2 is rotated about the y axis, the solid generated will have volume A. 257r B. 487r C. 1671' D. 641r E. 327r 7. If it takes 6 ft-lbs of work to stretch a spring from natural length to a distance 6 in beyond, how much work is required to stretch the spring from 6 in to 1 ft beyond natural length? (1 ft = 12 in) A. 12 ft-lbs B. 15 ft-lbs C. 18 ft-lbs D. 21 ft-lbs E. 24 ft-lbs 8. A uniform cable, 30 ft long, weighs 60 lbs and hangs over the edge of a tall building. How much work is done in pulling the cable to the top? A. 900 ft—lbs B. 600 ft-lbs C. 300 ft-lbs D. 1500 ft—lbs E. 1800 ft-lbs 2 9. Evaluate /\$21n\$dm. 1 7 A. 12—— 8n 3 4 2 9 7 C. 312—— n 9 8 Z 9 E. 3ln2—3 % 10. Evaluate /sec4zcdx. o 4 A. — 5 6 B' 3 1 C' 3 . 1 4 E. — 3 33—1 11.E 1 t —————-— . vaua‘e/(x_2)(x+1)d:c A. In §(\$+1)l+0 E:—(a:—2)‘+ln B. §1n|2(m— 2)(\$+ 1)| + c C. %IHI(.’II— 2)(\$+ 1)2| +0 D. ln|(:1:— 2)(:I:+ 1)| +0 E. ln|(ac— 2)(:L'+1)|-—1n|:v—— 1|+C 12. The substitution best suited for integrating / V 1 — 4:122 do: is A. a: = 2sinu B. as: 2secu 1 C. \$=§tanu 1 D x=§sinu E w=\$secu ...
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162E1-S2005 - MA 162 Exam 1 Spring 2005 Name Student ID...

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