A2 - Q Name(PRINT M ‘ StudentnIlD" Math 1A Midterm 2...

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Unformatted text preview: Q Name (PRINT); M ‘ StudentnIlD; " Math 1A, Midterm 2 Summer 2007 Instructor: Lynn SCOW Time: 50 minutes Instructions: 1. No calculators are allowed. A one-sided sheet of notes is permitted. 2. Show all steps clearlyr Simply writing the solution without showing work will not receive full credit. For steps that are not the direct application of a rule, it is required that you further explain your ansWer in words. 3. Give only one answer per problem. Do not give two answers, or else only the first‘answer will be graded. 4. Good luck. ((Do not write under this line)) ‘ 1. (20 pts) A water tank has the shape of an inverted circular cone with base radius 4 m and height 10 m. If water is being pumped into the tank at a rate of 8 m3/s, find the rate at which the water level is rising when the water is 5 m’ deep. [Recall: the volume of a cone of height h and radius 7‘ is §7rr2h.] \]:’\-K\T7(9\if\ 3 A _ l,— g _ it ,3» .’ Ki?- (.51335LHTL‘1 (55 0V“ 15‘ at 4+ = if: 131: S ' 35' At a _ ' _ \A(1‘):5 3:,p—Oqg, C, ELL, )3 (£1 , tzt' /. a 1 CW £it! “Eli—"j 3.. _ , all: Q. * r W 57"., NM. 2. (20 pts) Let c be any real constant. Show that f = $4 + 2:1:2 + c has at most two real roots. 9“ cmkméwhm, watt was ' at mm wag "Md‘l mots/ Ca“ mm >973. Tm €<>)ré;gfi$(j):o “was, / W05 €(x): 9(3) , ORA vaci 3C \3 _, dvngerc‘nfiafioig QM CHAA thhUU‘US . OV‘ Cx«j3 (03 cm Povhtrwvddl d" \{ o\\€€-<r{n‘hcxue Quflrjulw / bj Qo\\éf W613er Mfg V\5 a C, “A (le) §SOLL\ qu’fi’ $‘CQ\):_D Skm‘\qr\3 / SVALQ nyA {:«g QerubV‘Qre/ Lj along mare,“ To“: \f .caxm (3.3:) SQCR “49+ .J‘Vrafllo C‘ i Cam go g! mos+ gave at; {€04er . raids mots . PC"): “XE JVHX’ :HX (ml+'\>"éb _ A—> 54:0" or XQH= 0 I (\MPBSS‘L‘Q} M m 53 “Pathm “Mgr "U MVMJ 6:: rqa\foo’r/ Cmmokxdnm. ' MUS [AUX V\b W WO‘W ‘h/Db (‘QOJ rook—S . 3. Find the following three limits. , sings—a: ‘ 0" (a) (6 piss) i151) m3+$4 , O L: 9‘0“ C0376 ‘7‘ “‘9': : Xfl D 311+U\X? '0 l LH Q ’SMX : ‘m 1 Kat) @xl— \Qxx ’ Qim 9"“ “l : x,,>b )< x»—~>o ($1431 * l —l' : L ;\ ,— G+ Q , b , ln(x —— 27r) 1—03 ” (b) (6 pts) $332+ sinx f. \v\ (X— EMT) :— *OO" , ~ . \ 9m - ><—->&\T+ (3. cont’d) . . . 3/$_ Q V " (c) (8 pts) $1351+(c0§2:§) a : ‘ 3% KIA ( QWYx I (CBSD-X) )7, fido + 3/! E, \n (531x? : \V‘ X::o ( ; j : film :3 ‘ ‘m C581} .___1 me _ \n((§ga\x) X “5 O y 5kg) D 3 X“““’”” EH /Q\m 3 " Swfikx & K Cos Ax ,50 “WM—“MN .L : «QWVy ’ Q 1‘cxvx 3.x : D Kf>9 Thug 4. (20 pts) Find all points on the graph of f = V5113 + 1 restricted to the domain [—1, 1] that are the minimum distance from the origin and also those points on the graph of f restricted to the same domain that are the maximum distance from the origin. 0\ .3 (x~0)=1+(j—Dj: “NEW 611 = 3421+“); if t: 5"; f\ 3V\/\ 0/ X“ ’“ 01th ‘ 3 s 93) ~l l 6"“ 0&38 “(Mn . SMALL t ‘ “;/3 3‘6? I an Q‘oSb\°¥e"W‘°‘¥/MU\S o \ 4w. as W m taxis «’r y ) 3 g, ‘9 Max (MD \4‘ Che) & MCLY (3;: 3:}. l. c5005 . J 50 ‘l’l/‘Q ?b\n‘l’§ OK MWVMUM AWqu From (0 In) 123,: OJQV: <——I\/o)l <0") 0~wdx 9bln+-' W\O\X£W\0‘(Y\ AVG—“WU? W (0/0) as It (ill—5) ...
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A2 - Q Name(PRINT M ‘ StudentnIlD" Math 1A Midterm 2...

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