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Sol-165E3-F2003

# Sol-165E3-F2003 - MA 165 EXAM 3 Fall 2003 Page 1/4 GRADING...

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Unformatted text preview: MA 165 EXAM 3 Fall 2003 Page 1/4 GRADING KE7 NAME ______________J_.——————————— STUDENT ID RECITATION INSTRUCTOR RECITATION TIME ______,___.___————— DIRECTIONS 1. Write your name, student ID number, 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 exam. (10) 1. Find the absolute maximum and absolute minimum values of the function f (11:) = 337:4 — 41:3 on the interval [—1, 2]. '3 7. 9‘ g/(X) :0 I '2. X3; I‘ZXQ:O —-7 17.x?(x-1):O —-9 X: 0/ i ("CVI'I:%C\§VSF¢NS ,. __ kabsmn'n 0 f6!) :7 \$0) , ’L 3 AG abs max. f(7.) = 1g, , :346'4' F . 9(0) ’0 ‘50) _ absum‘L-xj‘ abs. min. (3) 2. True or False. (Circle T or F). The function f(:1:) = Ia: — 1] satisﬁes the hypotheses of the Mean Value Theorem on the interval [0,3]. T 3 (1» mt cu Winnie/e4» CL} X21. EULB) ”PC, (6) 3. Find all numbers c that satisfy the conclusion of the’Mean Value Theorem for the function f (x) 2 Va: + 1 on the interval [0,3]. @ RED—KO) : §£C9 o<c<3 f/(y): ,L.’ ) 2 X4" =7; [2— Ma 9‘ Id» 0% 0“.“qube ‘W rrviSSl‘yva OY" won%’ CTQCUI CHI/:3 It“ CAfYCgt’ Omi mars w boxes. MA 165 EXAM 3 ‘ Fall 2003 Page 2/4 Name: B4q,c)d. :, 0 Paint) 3/ anqu ’m uncut MMCA mo Wm’i" °“ “Mk ‘V’ w‘w'ﬁ (20) 4. Find each of the following as a real number, +00, —oo or DNE (does not exist). 93— L'H . x KNVR ~ (a)lim‘e. 1: m we 23—:1 1—)0 31H?) Xdo (.037‘ 1 '6' E tana: (b) lim : co z—+(§)— cscx Rim Tony :m 94m CSCXZQJY“ sihX:I1' . . J. Q)", vimx 0 (Ii—)OO de f" L’H J' 0 Lu» 4h; : 14m 1 " T30 w -:sn 0° I 2 s —1 £- L# —Sln‘>( +X <d>hm°°\$3+2:;‘m 1 : m—H) Y-éo 3x , . —'~ ~-~ WNW W .- ' — 7">O 9. CV >090 6 E 0 (6) 5. The number 6—1 is the only critical number of the function f(:1:) : mlnx. Showing all necessary work, use the second derivative test to decide Whether f has a local 'maximum or a local minimum at 6‘1. §’(x) = x4; +Qm><=l+lmx {’00 = 1): ® ,, (9 9w i (6') = €- >0 @ —@ (5) 6. Find the most general antiderivative of f (x) = 36“” + 7sec2 a3. MA 165 EXAM 3 Fall 2003 Page 3/4 Name: (18) 7. Let f (x) = we”. 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. [8: X e—X DOW“: QM 'X y NVC. k ti=0 —+ X6020 ‘3”“0 (0'0) 1 JAY 05% X10 4 ‘2):0 (020) §(-x) ': — xex no Saw-rel}? 7‘ X—Im X'IW'a’e LH ._ l 00 v *9120? =0 W 0“ ‘W‘ xe—X : —- 00 X—r—W -x 2‘- — e (9' —X) intervals of increase I _ i . g [(54) W" intervals of decrease as?) : 249:2 = 2:2— local maxima '3 local minima intervals of concave down intervals of concave up points of inﬂection 11:41. nuu 4.44;;nrvn u .LlJ/LJ. uuvu ;. “'0" L/ 1. Name: (8) 8. Among all the rectangles with base 1:, height y, and perimeter 20 in, ﬁnd the dimen- sions of the one with largest area. You must use Calculus. A r: X“; Eli l Qx+2~a :‘20 ——> 92,0,“ X A 2 x (10 ’X)@ 0 5“” cm ..._..7_ IO - ‘27 WM” X=3 °YX=IDI d1; 19:0 d _ . __ x— x=S Wklmﬂ:’ ,, @_o . l0 2 ’0 ”>127 (12) 9. A right circular cylinder is inscribed in a cone of height 12 in and base radius 6 in. Find the radius of such a cylinder with largest possible volume. (Let h denote the height and r the radius of the cylinder). (12) 10. A particle is moving With acceleration a(t) = t2+3 cos t. Its initial position is 3(0) 2 2 and its initial velocity is 12(0) 2 3. Find the position function s(t). (Mt) =t1+3codi m(t‘)=_;—-3+3stn‘t +C 3 ”(t)”;g- +3§mt +3 S(t):.g -3ms‘t r3144) Wlxmttoi 2 =0 _3+O+-D~5D:s ...
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