chang03.doc - 1. a. syms x y z l F= x^2+2*y^2+3*z^2-1 F =...

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Unformatted text preview: 1. a. syms x y z l F= x^2+2*y^2+3*z^2-1 F = x^2 + 2*y^2 + 3*z^2 - 1 diff(F,x) ans = 2*x diff(F,y) ans = 4*y diff(F,z) ans = 6*z P = 3*x-y+3*z-1 P = 3*x - y + 3*z - 1 gradP=[diff(P,x),diff(P,y),diff(P,z)] gradP = [ 3, -1, 3] gradF=[diff(F,x),diff(F,y),diff(F,z)] gradF = [ 2*x, 4*y, 6*z] f=solve('2*x *l=3', '4*y*l = -1', '6*z*l = 3','x^2+2*y^2+3*z^2-1') f = l: [2x1 sym] x: [2x1 sym] y: [2x1 sym] z: [2x1 sym] [f.x,f.y,f.z,f.l] ans = [ (3*2^(1/2))/5, -2^(1/2)/10, 2^(1/2)/5, (5*2^(1/2))/4] [ -(3*2^(1/2))/5, 2^(1/2)/10, -2^(1/2)/5, -(5*2^(1/2))/4] pt1=[ (3*2^(1/2))/5, -2^(1/2)/10, 2^(1/2)/5, (5*2^(1/2))/4] pt1 = 0.8485 -0.1414 0.2828 1.7678 pt2 =[ -(3*2^(1/2))/5, 2^(1/2)/10, -2^(1/2)/5, -(5*2^(1/2))/4] pt2 =-0.8485 0.1414 -0.2828 -1.7678 b. syms r s x y z f=(1-3*x+y)/3 f = y/3 - x + 1/3 ezsurf(sin(r)*cos(s),(sin(r)*sin(s))/sqrt(2),(cos(r))/sqrt(3)) hold on ezsurf(1.17768-x+0.3323*y) 2. a. syms x y T=2*x^2+3*y^2-2*x T = 2*x^2 - 2*x + 3*y^2 Tx = diff(T,x) Ty= diff(T,y) Tx = 4*x - 2 Ty = 6*y Sol=solve(Tx,Ty) Sol = x: [1x1 sym] y: [1x1 sym] [Sol.x,Sol.y] ans =...
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This note was uploaded on 09/04/2011 for the course MA 280 taught by Professor Profdecir during the Spring '11 term at Montgomery College.

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chang03.doc - 1. a. syms x y z l F= x^2+2*y^2+3*z^2-1 F =...

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