# S 16-1 - Math 200 Spring 2010 Worksheet#22 Name kt Section...

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Unformatted text preview: Math 200, Spring 2010 Worksheet #22 Name kt; ' Section 16-1 Vector Fields 1. Sketch the vector ﬁeld: - _, ' ‘ “Fax,”- (b) F(x,y)=yi—xj \1Fh=\5y‘+x‘ < yJ—x‘» {s Gav-Perditulav {‘0 He Fold-Con wed-or- < :99 and has 44-2 Some larva-HA. “242%!” ‘1‘6 (Jon-d1; hut-PL M Same y—coordt'ml-e. The meter: 5.2133. 03:17! a" m'ﬂhch‘cuur +6 4h€ berl-lon‘ued-W' (fly) and have Unli- levy-It 2. Let F(x,y) = —————--—(x+y,x-—y). Verify that F is a unit vector ﬁeld on R2 —— {(0,0)}. d .. ._i.___..... ‘ l a. 1, H Fixﬂ)“ ‘ m “(X-+7]: ~70; 2 m) G X1+1xy+7l+x “Duly-t), = ' War" = * 3. Find the gradient vector ﬁeld of g0(x, y) = x2 + y2 . Sketch the gradient vector ﬁeld together with a contour map of'qp. " -1. .1 t7le 3 's not de-C' at v ’ 3 1 L A I a l - M q) [311) 1 [X +71 (1;); 4‘15; (X1?) (1+- ? unath hut _ x— + “if” 9 r: else where all veslets 2‘ 7‘ - X X ‘1" x‘+"3 " ﬁ—L‘i‘ -' a. have length ) and x '17 Point- Quanta 10m». 14%? Origin. 4 1. ' ‘44,. 1 1 __ Qwrdel bu x + k center ( b, o) 4. Find the gradient vector ﬁeld of (0(x, y) = x2 y — y3. A plot of the gradient vector ﬁeld ,togeﬂier with a contour map of go is given. How are the gradient vector ﬁeld and contour map of on related? 1‘ A :-__ 4“ ﬂ _ Tl? SMieuf' \IE‘c-l-ors are P9f’Pekd:£ulur d‘o-l-Lelewi Cornea; lie gradient VELi-ors are, long) {aka-0. 4K9 1013.0 Cuwﬁl 0W!- ClGS€V.+°.?¢-¢L- O'I'hev and sigh-t where- 443 curve! (DI-N i cuﬁ'i'isﬂr QPM‘E. I — 5. Verify that the unit radial vector ﬁeld and inverse-square ﬁelds are gradient ﬁelds with potential functions r(x, y, z) = xix: + y2 + 22 and —r" , respectively. 7. ﬁx :9. L2 — J- l. 1.. 'X 1. "' 1. "' V“ 2M) 37, 327 ‘ {Mme My); WW5». Yin), ﬂxhyifﬁmp : M 2" l 1 g > I. g . m r, v r ,wem- Phat“ Mf‘peid Wing line claim vole gar gmdienﬁ) _, -' _, ‘2 _. -ln " . g‘tvecl-or-Ffolul W P l - I” 9r “1’ 6,. = \$3 )‘Heinwﬁersﬁ‘Wemm 6. Find a potential function for F(x, y) = (2): sin( y), x2 cos(y)) by inspection. < 1X85”), XLCoSly) 7 = 09179?) axi‘nw at u Therese, (Paw m X (0)13) : & xzsinly) —-—_..‘. 3 a.” __ .. 1- a . a __ gfj :— Ey 17‘3x1‘37)332*‘+#;;=xgj§1‘7 >2 x l- n'l‘ “9‘14. mﬂlk'lfw Shd'ifqa e e SWk-H‘d- FrD‘P‘ fun tion forE(r) = f—Qgr (Electric Field of charge Q), 3's?” “1:? A WWW?) : '5‘“ +%3 {‘32 K : -7 — :- “ “L z. a 2. \- '-‘ l- 1‘ as —"- " 99>[ 1(x +71%) {2:} t‘§(><:y+i )(2,)3~i{xlyii‘)7(12) k] t- '.\ " ' = e9 2 9 LE... to mw )’ Q II‘i-‘n’ Homework #22 Reread Section 16.1 (Due 04/16) Do Section 16.1 Exercises: 3, 11, 13, 18, 19, 20, 21, 23, 24, 26, 27, 29, 30 Prepare for next class session: Read Section 16.2 ...
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