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 = 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) a ’L 3 Ag abs max. fig) = 1g, , :346'4' F . ’0 _ absum‘L-xj‘ abs. min. (3) 2. True or False. (Circle T or The function f = Ia: — 1] satisfies the hypotheses of the Mean Value Theorem on the interval [0,3]. T 3 (in mt cu CL} X21. EULB) “PC, (6) 3. Find all numbers c that satisfy the conclusion of the’Mean Value Theorem for the function f 2 Va: + 1 on the interval [0,3]. @ Kan—Sic) : §£C9 O<C<3 f/(y): ’L’ ) 2 X4" "A? [2— Ma 9‘ 0K1 C'\‘.\"u“"k*Ur ‘W rrviSSl‘yva ova won%’ Crecut 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’l" °“ “Mk ‘V’ “*“23 (20) (6) 5. (5) 6. 4. Find each of the following as a real number, +00, —00 or DNE 'maximum or a local minimum at e~ . (does not exist). I . (a) hm 6L1 5-,! 'm .fix- —-.£_-1 t‘m ‘ z—)0 3111113 xdo mEx — 1 ‘ '6' El , tana: (b) 11m -- co z—+(§)— csca: 1 _ RN, Tony :00 (Cm ‘CSCX:QJW __sinx"1 ""9 “(a X“ ‘3 ‘ny‘L Q3 £225 0 (c) limxl/z (e, )*-_: exroo >r z-e :L (Ii—+00 Xflm f. L,” J' O A ? Um lit—z": Z '2. T20 M29- ”"°° £51 00 2 I , —1 1- L#- —S( 9:4. (d)hmcosx3+2:‘m nix: 91—}0 xéo .’L' *8 95 513 . —-msx +1 glnwro Jm «see a 7">O 0 The number 6—1 is the only critical number of the function f : mlnx. Showing all necessary work, use the second derivative test to decide Whether f has a local ® g’(x) = x4; +me:l+lm>c {’00 —_- l): ,, (9 9w Q (6') = €- >0 @ [9 Find the most general antiderivative of f = 362 + 7sec2 a3. MA 165 EXAM 3 Fall 2003 Page 3/4 Name: (18) 7. Let f = 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 Sameth 7‘ X—Im X—vav'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 _ l . g [(54) Wx intervals of decrease as?) : 249:2 = 2:2— local maxima '3 local minima intervals of concave down intervals of concave up points of inflection .L'LLL ¢uu J—JAbALAVL u .LlJ/LJ. uuvu ;. “by 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. (j A r: X“; ‘ci Qx+2~a :‘20 ——> 92lO—X X A 2 x (10 ’X)@ 0 5x510 cm ..._..7_ IO - ‘27 WM” X=3 °YX=IDI d1; A:O d _ . __ x— x=S Wkunx=" ,, @_o . 2 ’0 [5:27 (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). Let V Alma; I I Volume 0/ m ‘7“ I r V:TTV2ln C2.) (iv M—o: WNW-611v :0 0” GTH" 4—6113 (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 mew";- +3§MT +3 S(t):.g -3ms‘t r3144) \Nlnmt—o: 2 =0 _3+O+-D~5D:s ...
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This note was uploaded on 09/14/2011 for the course MA 165 taught by Professor Bens during the Fall '08 term at Purdue University-West Lafayette.

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

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