ReviewMath2224Fall2007_2

ReviewMath2224Fall2007_2 - FORM A Math 2224 Common...

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: FORM A Math 2224 Common Final'Exam, Spring 2006 Instructions: Please enter your NAME, your ID NUMBER, the FORM DESIGNATION LETTER and your CRN NUMBER on the op~scan sheet. The index number should be written in the upper right—hand box labeled “Course”. Darken the appropriate circles below the ID number and form designation letter. Use a No. 2 pencil; machine grading‘may ignore faintly marked circles. Mark your answers to the test questions in rows 1—14 of the op—scan sheet. Your score on this part of the test will be the number of correct answers. You have one hour to complete this part of the final exam. Calculators are not allowed. 1. Which one of the following equations describes a hyperboloid of two sheets? 7. ’z . "L _, (1)x2_y2+22_120_ ,_ 3L At «ea No be 01:13! cm. a 2 2 2 >41 Qa'ébvlwg '00 0 («W ith i (2) x '—y —z +1 = 0. "’ " ‘1 Z ,L (1L*\)z,\{zv:éz:l\!es @ @x2+2x_y2_22=0. 1425<M ’\“\l "‘9‘/0 '9’ M" aw \n mum (4) x2 —2x—y2 +22 +1 — 0. tum) ‘1 *1 0 9° XV?“ é sew/ac W “” \mfln . At a certain instance, a cylinder with circular cross—section has height 20 cm. which is ,ad CW)‘ ‘ « increasing at the rate of 2 cm/sec., and radius 10 cm. which is decreasing at the rate of d ( 74) . . . . m “a {fi— 1 cm/sec. Then at this instance, the volume of the cyhnder 1s (recall that the volume ,,V rad CU“ of a cylinder with radius r and height h is Turzh) 3h (M R demoblwy?‘ (1) Increasing at the rate of 2007: cm3/sec. :) C)\l : arrhdgfl‘ldlfi mm ‘ C (2) Increasing at the rate of 1001: cm3/sec. ' 6:” :zfmo :30 .L-fi—r if .6. '2~ (3» Decreasing at the rate of 1001: cm3/sec. : ; Zoo; (mg/a o @ecreasing at the rate of 2001: cm3/sec. ' c cheflcéwfi 3. Consider the function f (x, y) = xzy2 + 2x+ 2y. Which one of the following statements . . 7 1 is true. i. I (l) f has no critical points in the (x,y)—plane. 3), x : 0 g :3 (2) There is a pointin the (x, y)-plane where f is a local maximum. Jr"! :0 2401322: <3 lily-kl c0 (3) There is a point in the (x, y)~plane where f is a local minimum. , skez There is a point in the (x,y)-p1ane where f is a saddle point. fa seq 1 _\ c) x s , R Z D(—\_\3:\£¥x “MW zL‘ ‘ -3 \I 7‘ %\i# 961% [y‘fliAé‘q :‘DDLAI\>:\ Li Z\: “KLO v7 \{ c '\ ) $:'\ n ,- , saélch‘e, a d t Maw Revitawa we (Ln-Hm \Dofrfi'S -' 41x: 0 .F—yzo 234x79x3f20 , K Arxll 1X33W93X2Q =>CLWA V Mm? kg? P“? \J 2— —. ya =(\- a) r: m o ’36 ,1 l a; V 31 3 A? — — —- :0 1:) "-i— 9 E3)“; (fif‘fl_\ 3‘! "E U36 (MES: V ‘ — -— H L — ————- =>) ‘ :——’ V20! mesa/jg (4): 3(3)- (oar %(\G - (3a) V265 a" Z ' fl 73,375 7.) x: 3‘3 => max ,9; :ficm bow/“d0”! 1 5‘ "1: 3173 N- WMWWFQWW'WWWM_ I _ ‘ . an 5. The value of / / ehzdxdy is guww rCfixon I mtzegm‘n Hm ° W aw m m XX MR?“ (1) (e2—1)/2 <2) ('eZ—1>/4 <3) (e2+1>/4 . (4) (e2 —2)/4 -—-— ~ mm- w-m— ,, M“ 2 \/4—x2 Sh‘roif‘vw listen «93 .vAfegmh‘an 6 The value of / x/xz +y2dydxis 01m mg}: n . W x O 0 +0 polar COWOLCF‘Q. (=5 (1) M2 Ecumeolosrg; {2565327 TE 1 r‘ W/ V 17 2 @4n/3 :3 J0 f0 2 W_}r&9&r :j‘ S (ZJGSV‘ ' ‘ ‘ 3’ u? 1 (4)27: : '2' '. Zrlr:W.l/_.3 =_"/.~—<-> D~i05X£20&7’£m‘§ f0 ‘19 jo J 4 a lo .2/ 3 3 / ’ 7. The equation of the tangent plane to the surface x2+2y2+3zz=6at the point (2,1,0) is __ Z '1. (1) x+2y+3z=3 +(7<,%‘2:\=>424 1% +5? - (2) x+2y+32=6 {8M gwu‘jagl ~.i,(,c,\{\e\:g‘ x+y=3 ch/Lq'ctla‘fi33" \/ (4) x+y=6 1% (N10) (K4) '* 1v [2", 0) (y~2) 1 :z.{2,‘,0)(?-0)=’0 % : ,— T—x :th a... 1 100 12. Let an = — + —— and let bn = (—1)”an. Which one of the following statements is 100 :1 true? I (1) The sequence {an} is convergent and the series 2])” is convergent. «(v—>90 shah WM 21% aUmhaWO) SUM/S 'h hwy bfl1(v\)an @The sequence {an} is convergent and the series 21),, is divergent. (3) The sequence {an} is divergent and the series 2b,, is divergent. (4) The sequence {an} is divergent and the series 2b" is convergent. ‘ -_|, \00'0=’€fi‘% ‘ ' 0° (_1)I7217 . 13. The sum of the serles n IS ‘ 17:2 3 ovnd anZLZFO (1) 4/15 ’9‘ n (2)3 ( a)? “‘7‘” we 2% ='e*’5+" => «3’ (3) 2/5 H53 ’ 71353 5,; - _3 ’0 $ (4) 2 r, 3 0° n22” 14. The radius of convergence of the power series 2 "I x—l)" IS 11:1 " (1) 1/2 2 w (2) 1 “Ratio Witwan= ‘3‘ (Pom (3) 2 _ 7w. 1 . \ @“ \Oth-H‘ \(nq‘U/igya‘ (x—OVPv M \ .———— 3 // a t a“ try/7“ n2 few“ (to/*6 n7“ 1 j airflo‘Yfi"- Hm “.1.\><~(?:O~\><-‘\‘O<‘ rm an ' n—m ht ‘ ‘ frf all x be n22” n => 2 __. (m cw w au x . q - 96mg @4119 W mom (i3 , (2.))- @7 ¥o(wh{ch mu km W dgdmw (ML OLUOML 1Com wWhfl ~ Ham-3L0. mayw-c}emmm;recjm1.,_gn OKCMF. dded-e :3 _. _- baigmw a. M /\ Qfiékifik ‘ m-” —~ — v -w _ — m ‘ \/%~1>la/Y\Q/ ...
View Full Document

This homework help was uploaded on 04/22/2008 for the course MATH 1206 taught by Professor Llhanks during the Spring '08 term at Virginia Tech.

Page1 / 4

ReviewMath2224Fall2007_2 - FORM A Math 2224 Common...

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