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# Sol E1 - Z MTH'24'3 Examl gunmen-er:53 W 611{12 points...

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Unformatted text preview: Z MTH '24:: '3 Examl gunmen-er :53 W 611. {12 points] Consider the two vectors U = 21' ~3j+ 4k and _:. V=i—2j Find wr- —} E 3 k a) En? V:2+g+o=3’ b} mix: '1. -1 H - 3— 2 i. -1 J : E (oJrE)-j[ﬁ-rif)+l"‘ kw?) :_ L3 ; H J "'" I} o) The angle between U and V - A Mg??— U. if 1 (3 : _ . 559—19‘3” To 2* Mir-WU d‘i‘aE ‘ d) The veotor projection of U onto V4 Ae/__}_o_.._; —~ .4: '4 I/ Pr: U time? - VF : [j'if . E— 3 i}: W! it E null :é‘ﬁiiFrEJE-h —%.:H*1;a? e) Plot- theveotorsU U, V? Ux V and Prof? U on the same coordinates. {12. (1D points] Find the distance from the paint S[_1,21-3} to the plane“ 2x+3y+63=0 05:} 3?; 5; H T! =UF§N1m91 P.1(g‘ragd) 'r I Pa? .EJ- 31.? 73) Zj+91z Q3. (10 points) Find the parametric equation for the line in which the planes .1: + 2y + z 2 land I n y + 2': :—3 intersect. Y5“: *‘TL'V - “f, 4: '22 :-._Z’ ﬂ iii-ELI ﬂ (“53W 5'2- per? Taker; (image? __ s 3 ﬂZZE+§:—§f3:1 =55 8(5)}2—3'3) I"; ._....n -:——---— — - __.__| V -'— Vﬁli X W1 :- 1| 1 i :E(Q+I)*S(2'k3*htrlpz) 1I. "Pi. 1- {9/ X15? 1‘5 2 ‘2. “1— '9: :ﬂl—lb Q4. (10 points) For f{x,y} = 2x2 + 4yi +1 sketch the following on the some coordinates: a) The levelou-wee: f=0, fz-l, f=3, f=5. and x=0. b) The contours: f=1, f=3, fzﬁ. o) The surf-ace: z = f(x, y). :9 rt: A : 1:41 + of W CWW' ':1 % .o =1x1+wf do Log} '1. 'L Fri}. we 1:12:14:ij we: lleﬁ-Z‘i - 1 L:'5_-ﬁa .LJ:1X1+L£'jL*31:%—eki Kit-’P—i) Ezqglwt .r’ x "n (Q Q.%{ DHJ} gﬁ—aL Cf'ﬂggl r-g(_a:h‘s} .:_ J Ilia-'9“: rgl- (9 Q5. (10 points} .2' 2 _ a) Evaiuate lim :1: y 1 ELM—+£0.03 x3; —1 . : car! F (2 or Show that the limit does not exist: 2 x y . _ b) FDrthefuncﬁc-n f(x,y)= x4 + y: , (I.y_)¢(ﬂ.0) 0 , (Ia?) = (0,0) show-that ﬁrwﬁ): jgmﬁ) but f is not wntinuous- at (Dﬁ). .. - Qﬂmal— {=19} _ 5 6—: .. C M,JJ-£:¥L~; "adj: T ._ 1: fit“? Afﬁrm) 1.4-: Xv-h- “??H‘ 1+ hr”! ﬁthm =33 b‘j +|~J (961%: 449er PL? QEWWH— DUE )1 'r/gﬂc 5' p rt 3!}; {ML * 5?; (f3! 3.) jl‘ﬂm C(PVLL‘S/ F/QFM “L'ﬁﬁi LL QB. {1'2 points) 24} Find fm if f('x,y) = a“ *zysin x. F b) Find:at(0)l,1)fyg*+xggﬁ_g-m=0where z=zfx,y). __ ..__£‘j__ _ E MLH " F? " HH‘HX‘F-mf”? n x _ a .4.» C) Find ﬁat i=1, 3 = E Where gﬂxq} = \$344351, and ‘95:} .33. ‘5): 'bﬁ‘ 23W -—'—- F-‘pll—u. _ + I” ‘_..r-- “at i "at “3‘5 “at X - 3 {L '1. -—H -3.;<)~25i:e + '3ij ~szs \ / 5 1 _ .. = {5—1 - 2E ‘_ .— I '— ‘_ “EH—E EEC? (”1 TEL ‘5 + TH rv #156. (21?. {'10 points]. Determine the linear approximation ﬁx, y ) of the-function f(x.,y) = sin): may at (Um). Evaluate £03.13) and compare it with the actual vaiue of f{'ﬂ.1,31. C9 LfT—HV £(ﬁF‘LJ—tflw ‘Hﬁx—aJ-rfjﬁfgﬂﬁ it) :: a + mime“ .[pt-an -:mxsrn.~3\( half) {an} NE) a] := -— x @ 2—(5‘1r3): —§,| /-\' Chg-'51?) :— 8/ Sim-\$1M? :. .- 53.0933 l(@.|,1)f _ﬁ(a.l,g) ...
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Sol E1 - Z MTH'24'3 Examl gunmen-er:53 W 611{12 points...

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