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Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2, -2, ƒ(2, 2)) Z= B) Use the linearization to approximate the values of at the point (2.03, 1.99) and (2.04, 1.96) Approximation of f(2.03, — 1.99) - Approximation of f(2.04,- 1.96) = C) Compare the approximations form part (b) to the exact values of f(2.03, - 1.99) and f(2.04,- 1.96). Which approximation is more accurate? Explain why this should be expected.

Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2, -2, ƒ(2, 2)) Z= B) Use the linearization to approximate the values of at the point (2.03, 1.99) and (2.04, 1.96) Approximation of f(2.03, — 1.99) - Approximation of f(2.04,- 1.96) = C) Compare the approximations form part (b) to the exact values of f(2.03, - 1.99) and f(2.04,- 1.96). Which approximation is more accurate? Explain why this should be expected.

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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Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2,2, f(2, 2)) Z= B) Use the linearization to approximate the values of at the point (2.03, 1.99) and (2.04, 1.96) Approximation of f(2.03,- 1.99) = - Approximation of f(2.04,- 1.96) = C) Compare the approximations form part (b) to the exact values of ƒ(2.03, - 1.99) and f(2.04, 1.96). Which approximation is more accurate? Explain why this should be expected.
Transcribed Image Text:Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2,2, f(2, 2)) Z= B) Use the linearization to approximate the values of at the point (2.03, 1.99) and (2.04, 1.96) Approximation of f(2.03,- 1.99) = - Approximation of f(2.04,- 1.96) = C) Compare the approximations form part (b) to the exact values of ƒ(2.03, - 1.99) and f(2.04, 1.96). Which approximation is more accurate? Explain why this should be expected.
Expert Solution
Step 1

Given

f(x,y)=4x2+5y3

Now

f(2,-2)=16-40=24

fx=8x,fy=10y2

Solution a:

Equation of plane passes through (2,-2, f(2,-2))=(2,-2,24) is

z-z0=fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0)⇒z-24=fx(2,-2)(x-2)+fy(x0,y0)(y+2)⇒z-24=16(x-2)+40(y+2)⇒z=16x+40y+72

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