Exam3_Solutions

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

This preview shows pages 1–7. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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“; ...
View Full Document

## This note was uploaded on 02/02/2012 for the course PHY 2048 taught by Professor Guzman during the Spring '08 term at FAU.

### Page1 / 7

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online