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frz,y)= 1²-2xy +y? (8,9, 1) Le t 27yty-z =0 Fea,y, z) = ² 21y+y-z

frz,y)= 1²-2xy +y? (8,9, 1) Le t 27yty-z =0 Fea,y, z) = ² 21y+y-z

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you explain to me how it has z variable and how it becomes negative. Does it base on the sign of the point? The encircle part is the equation
4:11 Step2 b) frx, y)= 12- 2xy +y2 (8,9, 1) Le t Z- (,y, 27yty- z =0 Fra,y, z) = 1² 214+y-z Fa Cx, y, z) = 2x - 24 Fy Ca, y, z) = - 2x+2y Fz (a,4, z) = -| Fx (8,9, 1)= 2.8-29 = 16-18 = -2 -2 x8 +2-9 - -16 +18 = 2 Fy (8,9, 1) Fz C 8,9, 1) = -| .. The equation of the tangent plane to the Surface at (8,9, 1) is Fx (8,9,1) (x-8) + Fy (8, 9, 1) CY-9) +F_ (8, 9, 1) (z-1) =0 -2(x-8)+ 2(9-9) -1(2-1) = 0 - 2x+ I6 +2y -18 - z +1 = o -2x+ 24 -2 -| =0 z= -21 +2y - I * The equation of the tangent Plane is Z = -21+ 2y -1
Transcribed Image Text:4:11 Step2 b) frx, y)= 12- 2xy +y2 (8,9, 1) Le t Z- (,y, 27yty- z =0 Fra,y, z) = 1² 214+y-z Fa Cx, y, z) = 2x - 24 Fy Ca, y, z) = - 2x+2y Fz (a,4, z) = -| Fx (8,9, 1)= 2.8-29 = 16-18 = -2 -2 x8 +2-9 - -16 +18 = 2 Fy (8,9, 1) Fz C 8,9, 1) = -| .. The equation of the tangent plane to the Surface at (8,9, 1) is Fx (8,9,1) (x-8) + Fy (8, 9, 1) CY-9) +F_ (8, 9, 1) (z-1) =0 -2(x-8)+ 2(9-9) -1(2-1) = 0 - 2x+ I6 +2y -18 - z +1 = o -2x+ 24 -2 -| =0 z= -21 +2y - I * The equation of the tangent Plane is Z = -21+ 2y -1
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