165E3-F2009

165E3-F2009 - MA 165 EXAM 3 Fall 2009 Page 1/4 NAME Page 1...

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Unformatted text preview: MA 165 EXAM 3 Fall 2009 Page 1/4 NAME Page 1 / 18 lO—digit PUID Page 2 / 36 P 3 1 RECITATION INSTRUCTOR age / 6 Page 4 / 30 RECITATION TIME TOTAL /100 DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in 00 (9) 2. 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 sufiicient 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, calculators or any electronic devices may be used on this exam. . Find the absolute maximum and absolute minimum values of the function f = m3 — 3:102 — 936 on the interval [0,4]. abs. max. [fl )= .1 (a) The Mean Value Theorem asserts that for the function f = sin a: on the interval [0, 271'] there is a number 0 in such that (b) Find all numbers 0 that satisfy the conclusion in (a) MA 165 EXAM 3 Fall 2009 Name .__________________ Page 2 / 4 (30) 3. Find each of the following as a real number, +00, ~00, or write DNE (does not exist). ' 4 (a) lim 8m 1:. sis-+0 tan5a: (b) lim Egan—i. yrs—>0 $2 (c) lim (1 —tana:)secm. fl (1%»4 (d) lim sin a: In as. as—>O+ cos a: ‘ l' ——-———. (e) mi?)— 1 — sinm (f) lim (1 + g)”. {13‘900 l I I I l l 4 (6) 0 is a critical number of the function f : e—lml. Complete the following (a) If so > 0, f’(a:) = D ; f’(a:) is positive, negative (circle one). (b) If m < 0, f’(:c) = l::l ; f’(:1:) is positive, negative (circle one). (c) Atac=0, fhasa local maximum, local minimum, neither (circle one) MA 165 EXAM 3 Fall 2009 Name __________ Page 3/4 lnw (16) 5. Let f = Give all the requested information and sketch the graph of the function on the axes below. Give both coordinates of the intercepts, local extrema and points of inflection, and give an equation for each asymptote. Write NONE Where appropriate. Cy 2 1 1—— | I ~I— I +> a: —3 —2 -1 1 2 3 —1 —2 domain horizontal asymptotes vertical asymptotes l 1 intervals of increase intervals of decrease l:: local maxima .I local minima intervals of concave down intervals of concave up points of inflection MA 165 EXAM 3 Fall 2009 Name _—______ Page 4/ 4 (l2) 6. Find the cc~coordinate of the point on the line 633 + y = 9 that is closest to the point (—3, 1). (l2) 7. A closed cylindrical tank is made from three metal sheets (top, bottom, side), which are welded together along three seams, as indicated. The volume of the tank is 1000 cm3. Find the radius of the tank so that the total length L of the seams is as small as possible. 6 8. Findfiff’a: =2cosw+see2516,—1<:1:<1,andfE =4. 2 2 3 ...
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165E3-F2009 - MA 165 EXAM 3 Fall 2009 Page 1/4 NAME Page 1...

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