Sol-165E3-F2005

Sol-165E3-F2005 - MA 165 EXAM 3 Fall 2005 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 3 Fall 2005 Page 1/4 NAME GRADZNG— KEY Page 1 /17 10—digit PUID Page 2 /39 Page 3 / 18 RECITATION INSTRUCTOR Page 4 / 26 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. 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 device may be used on this exam. (10) 1. Find the absolute maximum and absolute minimum values of the function 1122—4 f(:v)=$2+ on the interval [—2,4]. {(0): _' abs max f(4)=-§— {G2}: 0 l2 3 abs. min f(0) = _[ — 4 (7) 2 Let f(:1:) = $2 + 9. Explain why there is at least one number c in (—1,4) such that 1 f’ (c) — Make sure to state the name of the theorem used. :80 MW and: «’1 (C (*4 _ : 4’(C) : 10(4)— (-4) 4 -(—-/) 0 - “'4 :‘é £9C>®7Wn2fiuém :: 7% Name of theorem used: MW MM 77% M kl 0 m 1 @"® "F hence! Mi. ER) MA 165 EXAM 3 Fall 2005 Page 2/4 Name: (5) 3. The graph of the second derivative f” ofa function f is shown. State the x—coordinates of all the inflection points of f. w &v}sw€lge£5+goocr€ot m“ git/(gene war 0 e - g \ 24) 4. Find each of theCf/dlelowm a rea num 00 r write D s not ex1st). / g ‘ — LH . \ (a) um (81“ x) a 003%" W . 4M _ J. m—+0 :03 _ f” 2 MM 3"@ SXI€M(H"L) e * m»; m—mo (1+1?) xsw e . 3&/I+-L) . 'JI“—-L C4) # Q Q?“ T's—X"? sém—A—fl‘flgj‘ :8.3 / <c> hm+<<sinw><1nw>> (33% fl” 5.14 Lain J- UHO Xa°+ “(X X9o+—MXA<: .._,€M; 543M sax _ GD "" x»; x 7.9:; “1'0 “0 (d) lirn _(tan :1: — sec 3:) ‘ N m—>(7r/2) @ It 0 ‘ \ \ \ ‘- 4 : Sax- W,“ ) = sax I L: {M “3X kegy aux cox , ‘ (10) 5. Find f if f’($) : MA 165 EXAM 3 Fall 2005 Page 3 /4 Name: (18) 6. Let f(x) = 11:61. 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. {(40— —Y€'—Y, MSW/x I'10" 9V6“ domain Lon. 1’9";on g3)? _-::_ . Lg? :— intercepts (O I O) f. :0 H.140 t Axexmx. g Symmery NON‘E # x-w» # I —| CD CD G) 4“ ) {asmrfp if} a“ x. A We horizontal asympmtes \—_g:_——__— €23 ’— 'X x ‘ X . P” ‘9 I _ e + X9 _ (flu/)3 vertical asymptotes NgNE CO / ' . . .F > o 42> Y > -| : W W453»; intervals of increase ‘F ’< O X (‘7’ : “525‘ intervals of decrease Room 59 r : : —I ‘ h \ local maxrma [5+ def Ted“: [emf )wm NONE {ll—I ) : «9"! local minimag— (“fl/wen»! o 1"”, 3 2 9 x+ Xe x : (2+ 708x intervals of concave down I, (~b<1/ ,2) (D ‘F > 0 (3) )t" >-2 : C (J intervals of concave up ' ( ___ 2 Do ) 7 G I/ / ‘F<o(‘—=)><<—2. :cD ,t f‘flf ? ¢ 01 in ‘ ,, a", Pnso ec1on (“2)0'26‘ ) f”(-2):O Peak} 5:! iw£/€m‘3f0w X:—2 , 3t: —2 ed MA 165 EXAM 3 Fall 2005 Page 4/4 Name: (14) 7. Use calculus to find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius 2. 297(2) '7. (6) 9. Find the most general antiderivative of f (:17) : sinzz: + 56"”. ...
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Sol-165E3-F2005 - MA 165 EXAM 3 Fall 2005 Page 1/4 NAME...

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