Calculus Solutions 24

Calculus Solutions 24 - Answers to Odd-Numbered Problems...

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Unformatted text preview: Answers to Odd-Numbered Problems Section 13.3 Tangent Planes and Linear Approximations (page 488) 9 Tangent plane 2 4 2 - a)- 2xo(x - xo) - 2yo(y - yo) = 0; (0,0,O) satisfies this equation because zi - xg - yi = 0 on the surface; cos 9 = ,m = dL, N-k = (surface is the 45' cone) zg+Y: +r,l 11dz = 3dx - 2dy for both; dz = 0 for both; Az = 0 for 3% - 2y, Az = .00029 for x ~ / ~ ' ; tangent plane 1 3 z = z o + Fzt; planeB(x-4) + 1 2 ( y - 2 ) + 8 ( ~ - 3 ) =O; normalline x = 4 + 6 t , y = 2+12t,z = 3 + 8 t 15 Tangent plane 4(x - 2) + 2(y - 1) + 4(z - 2) = 0; normal line x = 2 + 4t, y = 1 + 2t, z = 2 + 4t; (0,0,0) at t = - 1 2 1 7 dw = yodx + xody; product rule; Aw - dw = (x - xo)(y- yo) 1 9 d I = 4000dR + .08dP; d P = $100; I = (.78)(4100) = $319.80 2 1 Increase = - = &, decrease = - = &;dA = Adz - S d y ; 3 23 A@ M - Y ~ ~ + ~ ~ Y Y ,/z'+y' 25 Q increases; Q8 = - y , Q t = +,pa = -.2Q8 = El 3' Pt = -.2Qt = $ ; Q = 5 0 - Z$l(s- .4) - $(t- 10) P8 = -Qu = 2 7 s = l , t = l O g i v e s Q = 4 0 :...
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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