DIMITROV_MATH_203_092QUIZ3

# DIMITROV_MATH_203_092QUIZ3 - \$01 wmﬂ Name Math-203 Spring...

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Unformatted text preview: \$01 wmﬂ/ Name ....................................................................... .. Math-203, Spring 2009, Quiz #3, Time = 55 min Dr. B.Dimitrov Please show your work! Circle ﬁnal answers. 6 6 1[2pts each]. Find the limit, if it exists, or show that the limit does not exist: a. lim _ y ‘ (24040.0) 2:3 +313 ’— oau, W 3 3 3 S @714 @‘fg—J; 57"” (X 3'93527 MMMMLJW ("13 90/0) egg—9pm) I A; b m “9“ gm 5X+#9[/X9+y"+/e +4) ' (I’m—40,0) Wm 5' W 61'” 7’5”) “Kg/+15 -6’)(Vx"+g"+lé M) Mkaea/Lf/ ’ 2 L ’l C¢+b)(¢ 14):.4 rbz - [39/ ‘r 27/ {1/ p—————- 2, 39)”??? X 7 #5 6496/0») 0M wig/preach. =0,an 5;) 1637A! :_ O _ XXL/+3 0? _ Z [9/14 ng,ga0:>£rwﬂi 5790 iatu 33,9 “I '. 1' d hm my2 + y22 — 322:2 ' (ma—«0,0,!» 2:3 + 113 + 223 ‘ a+§~o 0, 2: L0 2»-»')O 67"“ . MK ‘7' ’ ﬁzz-9a 0+0+222 3 5 3 x 0m act/:2, 2905-; aw 2 +&—32 [email protected] a? _._w’ Zea 23+E3+233 2—90 N 9 2 2pts each . a. Use implicit differentiation to ﬁnd Q5— and ~63 for the function z = z a: deﬁned b the e uation 8x 31/ . w“ V q. i sin(a:yz)=x+6y+32 , IV bx; / QBiCXyQ[;2fX?2XJ:l-f32x =9 2: 9‘24955’0'33 J! X9 dagggg) -5 1/ b. Find the values of zx(a:, y) and zy(a:, y) at the point (0,1, —2) on the surface 2 = z(:r,y) deﬁned by the above equation. CD 3[3+3pts]. (a) Which surface (identify and name it!) is represented by the equation x2 + 9g2 + 42 — 4 = 0? (b) Sketch the surface. I ‘ E‘ Mﬁmrwia/Hm LUZ- «(>: —X2‘ﬂgz 2-/:-_£5\;zi @6541 ‘c , a“ a. ‘r My 02):,12’9, ('9?ka ML ("/91 O, 0W 1W9? 5[3+3 pts]. Which surface is represented by the equation —m2 — y2 + 22 — 42 + 4 - 2:? S e ' AAA. - "- VV—t " Sfuamé (3,1 , v 2 2 “(X 2+2z + ) —5/ +52 49:01; I (“*92+117‘-(2'2)2:/ I j ky/Wbaggxx 02;)? S ' (_ a 0/ 2) N‘ ' v I 6' Let ﬂx’y) = “Two-9Q! L1“ ( — 113 — y2). a[2ptS] Evaluate f(\/§, 1)_ I _ HIE!) :— w5’1'03>&(é “54%: @SP‘U—G) €42 b[3pts] Find the domain off, and sketch it. ’ “‘J WcéZ/s {16346 I a? . t , Imam Fm {ﬁoﬁw‘i a r, g :ac-H 9:38-th _ Cweeémwbug'l); 9oz+<72<6 - c[2pts] Find the range of f. C” 3 (—00) 7564 7 (Bonus 1.0 to the Final!) Identify the graph of the function f(a:,y) = m2 — 2g2 + 1 and sketch its -1, 0, 1 and 2 level curves. -~ ma, £ __ ~_- 2— 2 ,_ .. 952 2:2_ \ A / épg 2:)(2‘232Jr’ Z lac 2/149 —— + ,/ a ‘2 \l {(3)2 [2 [on «2+1 2:; —A/v/E¢/V/99E&\_: 1-! Lo 2 “I : K2”? :4»me . A .L, _, L memboémf’ p %;E__5Q13_( A new AW“ (MM W7?“ W M I L). ———~» ...
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DIMITROV_MATH_203_092QUIZ3 - \$01 wmﬂ Name Math-203 Spring...

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