Exam3_Solutions

Exam3_Solutions - E l’, E MAC 2281 004 - EXAM 3 Name: The...

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Unformatted text preview: E l’, E MAC 2281 004 - EXAM 3 Name: The exam is worth a total of 150 pts + 20 pts bonus = 170 points. Calculators are not permitted. Duration is 85 minutes. (1) (60 pts.) Calculate the following limits in parts (i)-—(lv). a; . w— 2 »5 Q Veal (z) (15pts.) llmxal-{Z—j—w (4 “*“L‘” w» gee: x —2x2+1 ‘lwl‘t”? Q 63,. Kowlomt? «w»; :1 Kim fix thx t1“ M e. M 43;?) X~§4 égefiw é” “a D" Q @flf‘; qoxgwjg qgwlg r: was , {waaw~ A. N y» W ( *#~>1WW' am a» he W ’ “mes 4.4%me ,4“ m4 2 W xealzfime 52mg 8 2x -— Sin(2x) .3; “my 3: ‘5 2;: ex — e‘x — 2x “ (ii) (15 pts.) limxao (iii) (15 pts.) limxmocel/x —- x) (:3? 05 an» $53) :«Qim x4372?) (1F. 06-0) Mac 4/? O A z ‘ a em 2; (1.? W) 2 WWAWW Q gigaé “ “3%? : QJM :: é/x “gag xe‘a‘é m fi“%§é x 3 (2) (20 pts.) Find f iff"(x) = ex + 5 $100+ 20x4 aw}, f’(0) = ——1, and f(0) :0 x - Ls» fig ’/ x‘ " \ QZQXW w wig J; (K): e “‘3” E} 5m (20 + E: W 1 E 5,13% *3: 5’; jay zigzag“ 4} am 29% w x 4/3 £3 a v Q x gr. C .gibfl : («gmgcfig (fl3+2© “f A % $1031: a: + Q a» Q m? 5;, wt: 1:" ‘3’ 5 “AFC « Tkfifiggwa/ r 3,; , 3% w $50: 95% mm: fig :3 i4 4 1». c5 :“VAflZ ¥Qx g E W 5 :gxmii} 5 Q “ 4/3 3% 4‘» T; 01w; €23 3 . (3) (40 pts.) You want to construct a box of volume 60 ft3, whose base length is 3 times the base width. The material used to build the top and bottom cost $5/ft2 and the material used to build the sides cost $3/ft2. Find the dimensions that will minimize the cost to build the box. (Argue that the dimensions you found minimize the cost.) l, r, x e) is :‘Q ‘ ’ “coaxial {$6.1M ' 30:3 mxmrmzte r \XIQ, Wax :% $32») a x a ‘2 / 4:7 as? a a 951 x /% we? (“I a s l \ “fl” 7;, “WT/fir“ : 7 wg f3 M \ \ It; ( :3 a QEACN’EQi 331;: Q“ ~ 2 \ l; i“ 66:; \ v} 3 (25 Walk x2—5x+4 (4) (40 pts.) Answer parts (i)—(viii) for the function f(x) = (x__2)2 i) (2 pts.) Find the domain of f. i) (6 pts.) Find the intercepts (if any). iii) (6 pts.) Find the asymptotes (if any). ( l ( (iv) (8 pts.) Find the intervals of increase or decrease. (v) (4 pts.) Find the local max. and min. values (if any). ( ( ( vi) (6 pts.) Find the intervals of concavity. vii) (2 pts.) Find the inflection points (if any). (5) (10 pts.) Let f be a twice differentiable function with f(——-1) = 2,f(0) = 1 and f(1) = 4. (i) (5 pts.) Show that there exist two numbers a in (~1,0) and b in (0,1) such that f’(a) = —-1 and f’(b) = 3. (ii) (5 pts.) Show that there exists a number c in (~1,1) such that f”(c) > 2. (Hint: Consider f’ on the interval [61,19].) (0 %u tine: Mean Voice: fibeorena/ fleece are? own iii» if“: Q £33 0 06$ \Q to (0,4) sue/b float may : igliéié 5; are mg) {:3 AM?) ‘i mjciiifiiétotgmg wwfim ’1 W ‘ t T \ I \ “ Qagig c (LL) Since is; JCWZQQ Cgfiigéf‘éifiiflfigkfig 30 g; ‘59 Ajggfi‘i , WA. fl \ a flumggf i: gm P33 iota, Macao \fgaéua {twee}??? cine; e if; Ci» Sud/x g” c were?) ai<aa<Q<b§i4 WA .30 LL» x» Ii Thereigm/ f (a) - E: m a“; ...
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This note was uploaded on 02/02/2012 for the course PHY 2048 taught by Professor Guzman during the Spring '08 term at FAU.

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Exam3_Solutions - E l’, E MAC 2281 004 - EXAM 3 Name: The...

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