OleMiss - Math 264 - Study Guide - Midterm

Unformatted text preview: Ausly guide: Cal-4- zum I 1. Compute .. the cinctional derivative of f(x,y) = Ln (8 + m2ty) at pcs,-) in the direstim i Solution: <12> AF Cny - 3+ z2ryt 8+**y) P4, 3) = (.58249 C L-)= =32 K OHA (4,250V+8 , la = df (4-1).7 E (TE SA- TABS 22 ) 'directional deri sative i D. 9.2klose... Legrange Mullorplieno.. to.- flrd... the maximum & mainimese values.i. [(4,19,2) - Erre subject to . atty 2 = 16 Solutions fory): 22 122 g(xyet): X2 tyd 322-16 > O.yf'lky, ) - 79 (x,y,r): <2,0,2 => < 28, 29, 62) No. MU 2. - 4.2 -D O : Y- 22 : 2 --- here in 22 - 2 = m, 22 C 1- 32) = 0 eitu, TAK L : A : 1/3 ZOD/3 - /3 Take 2,0 2y =0 in ackoy, 2. , * * = 4 920. -- put x=38 yao in guy,t) the required point are 4, 3,2 + C+ 3 2 = 16 (3.0, ),C3,0,-D), (4.0, and (-4,070) .. IVF 85, 0 223 + 73j* 615 1847 25ja 503,0,7%): 2533 Therefore, Maximum value = 2% fur ) - 4+2 = 8 - ------- Miniro.rr value fc-90,0) --4x2 - B ..... - -5. Solution: find equation of planes passing that through ,-, 3) is or thagonal te plates 2x+2y-5res ard -x + 3y +2 2 33 ------------ Normal of the plane 22+2y-S2 2 0 : *: <2,2,-5) _ , - x^3y + 2 + 3 : 1-1.3, 2> Nos w 2:n ny - <2,2,-5) xk-1, 3,2) = ( 457(4-5), 5+2S > 413, +5, 82 : 419. 1, 8) lot, M(x,y,r) be a point the plane then AM (x, yts, S2-3) Hruly ---- .7 -0 *, (, yes, z-> 19, 18) 19% + 8z - 240 13x +y + 3x - 19 20 she the plane required equation f --