Math 20C Midterms

Math 20C Midterms - Nat P Discussmn Eamon N0 “Mg Time‘ “rPM TA’S name 15cm Wk/L;‘ Quiz 1 Math 20C Lecture D(Fall 2007 OOCLJOQ Duration 20

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Unformatted text preview: Nat P. Discussmn Eamon N0: “Mg Time‘ “rPM TA’S name: 15cm Wk; /L;‘ Quiz 1, Math 20C - Lecture D (Fall 2007) OOCLJOQ Duration: 20 minutes Please close allo your notes and books, tum. 017 your phones and put them away. To get full credit you should support your answers. 1. (5 points) Find |é|,a+' b,a'—/ 13123 and 3é+4b ifka : i_ 2j + k and b =j + 2.153 \____._-— —..,—-—-# a, OE“) : }“3” {-{J-Pj r}— 1/ J; L/ a- "ll ff, 5 \ /J I z ) 4/ J; x _. a ~ i. 1" L5; IF-h‘:| J _ _ "1.x '-.\ 14 2. (5 points) Suppose that a % U. 1. If a - b = a - C, does it follow that. b = c ? Answer: YES or@ 2. If a X b = a X C, does it follow that b = c '? Answer: YES or '5’ /" E lor NO ? 3. If a- b 2 a - c and a X b = a x C, does it follow that b = c ? Answer: Hint: For 1. think of perpendicular vectors. For 2. think of parallel vectors. For 3. use the angle interpretation of a - b, a - c, a X b and a X e. 7 ‘-. g, lei-{await ' < l i f L‘ > D ‘ ( r If ‘l _- {___i,\ [t‘ I won r---> . ,IW J a and HI?" ml: .51: f p x r f l “5/ Pi-(i(1.{_'-.r_"l "€066 ': rILl ____——F—————_ - . .. ,_, .VH. Plufw‘alfj Il b — at. r r: C‘ I .1'1:-"‘|k..'l,l'l 4 i' “I x g 1 f l O mom or g, f .‘ r_. .LL : J - I PI ClOC‘JIm Dog Time: H—SPLJ-lbndluu. Pecujcuqng‘t Quiz 2, Math 20C - Lecture D (Fall 2007) I) u r '0 firm : 530 m in.“ 1'. (35' (:3 Phsnsr' duh-r (If! your “.0105 rmrl hunks. f-um vfl‘ your phones and put. them u-tmy. Tn grit, fufl wrath! you .a'r'muM support yum‘ (lflfi'h‘lc?‘.‘?. 1. (5 points) Find 3 Immmntrit' vqllaiion for HIV i-illlifiILJil-lfi—LLLJ-LEF (flll‘Vt! with Lllv lit-F paranwtrit equation .r = z" " ('05 I. y = c' ‘sin 3. a = r" a 11mm (1.0. h\\ K: Ftcbg‘}: (M0115 4:9“fgmt th: --.-'. '{ ‘--..._‘_‘_ -—._ _. — -- --—-__ __ _ ""-——-_.____ — _ FFJL- \ x _F _ t I '— 9 t I f C / _.-’ "' l | ,L W %:€'tgflf 1 k #1 *€'t(bei {E’X“ -(”‘*) (flQLJ - fl 1'”) C _ ».- t '3. 'd *‘C _ , Lfi._e~—-—#::7~- I”“’th'4* A :xc +crt 1/ 3 Yr + I? t 2. (5 points) Find :1_n_r2(1113.ti011 of the plum! that passes through 1 1- mint [—1.2g 1) and contains the line of intersecfzinn of the planes :I.‘ + y H z = 2 and 2.1: — y + . z = . ‘ 74 .2 ‘/‘III—‘/ " -‘ :f' )0“ iii-2 (PMQMB m(><~><u‘+b(Y—‘/o3*djjt). '— u’ M. Q1. 3X lj‘455‘ (3 u I.132“! /1r \ Hl> t; ./3.p1.':3> Z\,"JIL’> Yfl/I JIL+74-t<|'l"> 7“ <\:‘):L’1’7 4 c/f'tIfoJ 2 ~ H497 C» 1J0") rag-0‘) 4“ c «wager-1 .Wm . \ J F‘ r — ~ :( :fifi/‘V‘C 3’QC\%“('|§) "* ‘00? 'M—r 2) ‘ (wt 1) f L , \~, .._\;@ (I ) _.L Q (_ D Jgfi—ji-_i—j>—H1-‘(-—I_L‘+ I (J T ‘ ‘05 Limb} J (12344;)? K Nax'. I Discussmn 50813101] No: DOC Time: 4—; TA’s name: Pol?! n no HO L05 Quiz 3, Math 200 — Lecture D (Fall 2007) 5;: Duration: 2!) minutes / (2 fr Please close all your notes and hooks, low-o off your phones and. pol. them away. To got full credit you, should support your answers. 1. (5 points) If j'far, y) = 3'2 + £1372. find tho gradient. vector Vf(2, 1) and Use it to find the tangent. lino tn the level curve [tn-y} = 8 at 1:110 point. (2. 1). Sketch the level ..('.11th2‘ the tangent line. and tho. gradient vector. 1/503) : X24414)”- ,g-V (my) .anLLlYl eff/2.x) r 2(2) MW)" 4’}; UN) = J” 57".) A! % L4 F 4 I" “” ,/ r) -— lfifi‘l ‘9 {’1 : ZX’I— # q _ aE__/;;__...-.—- — ' r, x .- (V, H. \ 2. (5 points) Find all the second partial derivatives of the function “(5315) = c’“ sint. (Mg, 14:): L9 "5 Smt ruzs?“ gig : flea—3 sin-t ‘55: of; am I... _ 1. f - f Zil‘ fl 0’4 49 U“ ’“ 521404 M $21: z+ni “ML :1 bk Raw Ka-lz/ ’“ 2+ 11 [x ( 4 \ "3} (+0! 111 amean «H14 2—,)! “‘11 ch ’Q/J %I+Lo)g " O O X / ’ .1} [cu—L} Shirkflg h” C H “31“” Mg ” “X 7:l\ ’C] n;% (sz 4'". Z+flfx ?+k0}"’fl“f7x 05-h '- I'd. fix _,_ (1‘!) m 3/5/ [:I\ L? 1139 5—if—_,x~ L L 1:; z M‘l -; h 2 zkznk‘hf T‘ %h {V mh-J‘h 0...: "j’ 0" ‘E. J \ ._ -7\ le NJ» h’fl‘h J} Ih 5m 4 4k 2 2 z + hxfi, “M fix = WWW” ‘{a S H S 0‘s: 3 r S g : (flu-13)} = a 71m: am no 3+fi.3:p—1_,f£+1_,;1: : (($10 semen unuluugm pm? mnmgxeu: 011110qu am plug (51111061 9) '1 'Smms'am mofi poridns pgnmgs not? fipQJJ H‘Hf 1230' OJ; 'fimm) mqu we! put; sauoqd .mnfi. flu urn; ‘S'yooq pun sawu .mofi. HI) 39033 351);de yam-mm ()3; .'mJ;;m.mg (L005 H93) C[ a-Imoe'I - ooz qu ‘17 2m?) “(WOO fluwwa :omeu 53:11 5—41 3111:1565me uonnag uogssnasgq <7/ 2. (5 points) Use Lagrange multipliers to find the maximum values of the function f(-.T.. y, z) = 2x + 63,: + 10:. subject. to the constraint :52 + y? + 22 = 35. £(y.\j.§3= Zx-Hoxj 410;- flu-219‘): xuwa’ws _______________‘_‘__- d) 2’ 2A¥ @10:)}\\1 C7“): 2%} PM 3*)xx{ 5’)? ,L a C A:X,J ski-"VJ: 1’25’ r 1 1 7,» :1 j 3: (VWYI23 : JP (A) (A) V CI c i1 J’ 3;: Jr a: : 5C 0% ~ - x 3r- ; A?) kJ/A) @ 35> 3‘5 X2 \:)\2 Wm! VfllMiS‘ 3“ 3A __ f]; {LAT ...
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This note was uploaded on 12/25/2008 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

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Math 20C Midterms - Nat P Discussmn Eamon N0 “Mg Time‘ “rPM TA’S name 15cm Wk/L;‘ Quiz 1 Math 20C Lecture D(Fall 2007 OOCLJOQ Duration 20

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