Sol-165E3-F2008

Sol-165E3-F2008 - MA 165 EXAM 3 Fall 2008 Page 1/4 NAME G...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 165 EXAM 3 Fall 2008 Page 1/4 NAME G RA G H E Page 1 10-digit PUID Page 2 Page 3 RECITATION INSTRUCTOR Page 4 RECITATION TIME TOTAL 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. Please write neatly. Remember, if we cannot read your work and follow it logically, you may receive no credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators, or any electronic devices may be used on this exam. (10) 1. Find the absolute maximum and absolute minimum values of the function f(x) = (m2 — 3)e_m on the interval [0, 4]. -')( ‘ EICx) —.- (x33) 6' (+1) +20} € “:9. -1_X1+.3 #279 v I €130 =0 3 —€PxCx1—2x~.-'5)=0 —-—? CX*3)(X+1)=O ""> “=3; ‘1 5(1—1 mot {VI so) = '3 .313) : 6 e—3 '5': % -4 {(4)=1’5€ =% l (9;, ? 7 ? I» < ~§é3 -—-'7 1—2— <6 ——7 £2246 yes‘abs max f(3)=-_%'§. abs. mm f(0) = —3 Q (10) 2. Find all numbers 0 that satisfy the conclusion of the Mean Value Theorem for the function f x3 — 6x on the interval. [—2, 2]. {2C} 2 M® \Lov we 66 (4,2) 2—92) 9( " Ll. — 4— , 2 007.3% -—G g G— __ ...—; Cizi ->C='i2" GC'G—‘Z 3 MA 165 EXAM 3 Fall 2008 Page 2/4 Name: (30) 3. Find each of the following as a real number, +00, —00, or write DNE (does not exist). (a) x+sin$ A___. _Q__”_ GP]; mJL lim —__. .— m—>0 x+cosx' 1 NFC m—>(g)+01—s1nx xfi a “9&4. 0 f E _ L H a g (0) 11m 1 02081; ___._ ‘m .EEP—Z‘ =1 :1" ' flxfil'4 5-31" 112—)0 Om 2 x~fl X 2 Q— T ,— , 32'- L6,? 30 'L H _ , )f w ' :1: 'm (d) $1320 (mm-)2 00 L’H —-' l 00 1____ xi ~ (>0, 7‘ F? I 'X—iboo 2"]; '- 00 E 3’. 7V 1' 1 2 3w' 'x , __ «9.1m (e) $3514 + x) _ _ {3 “0+ a a” (10) 4. If 1200cm2 of material is available to make a box With square base and an open top, find the largest possible volume of the box. (Let x be the length of an edge of the base and y be the height). - V 2. 73-1—4903: 1200“ -———> *3: igoo'xm V 2 4x \, :x -; 2:3 00 'xz' 3&1 if" .sz 1%._._:..—~ v=300rxfl 3 O<x 41012 4x 4— AV ,. 2. w ’ 309-2')‘ ® 0... n. dim—«we $20 -—-) ‘X- :400 47:20 ‘x O 20 {0‘63 X WWW .. . .. 4.00.22’ 0 -— o o . v 4 MC“ v “300 20 4 '63030300 400061173 E MA 165 EXAM 3 Fall 2008 Page 3/4 Name: (16) 5. Let f(:c) = (326:)? 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. Domain: (1.4L 7(7é-—’L X—(‘hL'Z \A:O~.; 29350 .4 xstfi tg—I'vd. {70:0 —-) kd=g Sséwmutfj Y.— Wang. “Aw: 2'w:=co x«>60” (W) Give all the requested information and sketch the graph of the Xqfl) {it-H)z “ Verb As. xv-d , ) / H.A: Um 22% =—1 t’ 9 (4,4) x—; too Lx+\) ' domain ('00 ’1) U G1,”) @ HM. As. = '1 _ ’ gm: 6W) (an) (0,2) @ z M2 Symmetry N o N E [79 I _’ Eéfg‘gfg horizontal asymptotes \a o; .. '1 @ Foo W; vertical asymptotes rx 3, 1 Q) 1%; v ’7' intervals of increase .)?-.intervals of decrease (_ no I A?) (‘1, 00) @ yaw; {X‘fozn Q:(>:+‘z)3'()m :“twr-l } " 6 ‘ +1 . 2X+2 (36“ 2'2 local max1ma N O N E @ .__' _,. V __ X'H __ .. 4; -20 local minima (,2) -2) (11> (x-H)" _ 2 fax +5) intervals of concave down (’00 I _. @ (x+|)"' ' 'te als ofconca eu ,5 '4. .. on a; W v v (V > <1, 7 69 ’P; points of inflection G, 5;) __. 22: 2 9 ‘Oli -E , 2—e—£>"_ 2—:- flea—26” g(2)"'—-(-:2§-)—i—’— i4 .. 9 .. 4. MA 165 EXAM 3 Fall 2008 Page 4/4 Name: (10) 6. Find the area of the largest rectangle that can be inscribed in a right triangle With 9 legs of lengths 3cm and 4cm if two sides of the rectangle lie along the legs. (Place the .vertices of the triangle at the points (0,0), (4, 0) and (0,3) of the (3:, y)—plane). 3 D 50‘ 2 Kym/Dr 04(9) : 26’2"?) (5) 7. A particle moves in a straight line and has acceleration given by a(t) = sin t. Its initial velocity is 'u(0) = 0 and its initial position is 3(0) 2 0. Find its position function 3(t). Mia-7 :0L(t)=<5/ht ma) :- cost +— C ha" "—’ -'l. "it—C —-—a C'z'l rum = . wit + 1 S’fi’):‘\)(t) :vCfis/t’i’l NFC ho" gg? t: rg-OLmt for :g-aDza SUP—$19113 +t E] 10 (5) 8. Evaluate the integral / In: — 5Jda: by interpreting it in terms of areas. 0 5 "" '* ID _. IL 5— p .é/x«5(olx ': 37:5”? -\—- 55‘ :1 2‘? M > W V 25‘ )6] (4) 9. Find the most general antiderivative of f = V4 103 + V3 :34. ...
View Full Document

Page1 / 4

Sol-165E3-F2008 - MA 165 EXAM 3 Fall 2008 Page 1/4 NAME G...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online