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A child seat is modelled on the surface z = g(x. y)= 2x +5y. One end of a strap would be at the point P(-1,1,3). (1) Find the partial derivatives g,(-1,1). g, (-1,1). (1i) Find the equation of the plane tangent to the surface at P. (iii) Calculate the gradient vector Vg at the point (-1,1).

A child seat is modelled on the surface z = g(x. y)= 2x +5y. One end of a strap would be at the point P(-1,1,3). (1) Find the partial derivatives g,(-1,1). g, (-1,1). (1i) Find the equation of the plane tangent to the surface at P. (iii) Calculate the gradient vector Vg at the point (-1,1).

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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A child seat is modelled on the surface z = g(x. y) = 2x +5y. One end of a strap would be at the point P(-1,1,3). (1) Find the partial derivatives g,(-1, 1), g, (-1,1). (ii) Find the equation of the plane tangent to the surface at P. (iii) Calculate the gradient vector Vg at the point (-1,1). (iv) Find the directional derivative D,g(-1,1), where û: j. /13 (v) State the direction from (-1,1) for which the surface has maximum slope. (vi) State the magnitude of this maximum slope.
Transcribed Image Text:A child seat is modelled on the surface z = g(x. y) = 2x +5y. One end of a strap would be at the point P(-1,1,3). (1) Find the partial derivatives g,(-1, 1), g, (-1,1). (ii) Find the equation of the plane tangent to the surface at P. (iii) Calculate the gradient vector Vg at the point (-1,1). (iv) Find the directional derivative D,g(-1,1), where û: j. /13 (v) State the direction from (-1,1) for which the surface has maximum slope. (vi) State the magnitude of this maximum slope.
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