Question 2 Define the function g(x, y) = [4 – (x – 1)²][1 – (y – 2)²]. (a) Find the local maximum point(s) of g, showing the test you used to determine its nature. .1.. (b) (i) Determine the linear approximation, g' (x,y), of g near (-2,1). Determine the second-order Taylor approximation, g"(x,y), of g near (-2,1). (You do not need to simplify/expand the approximation formula.) (ii) Estimate the value of g at (-1.9, 1.2) using g and g'respectively. Compute the error from each approximation and comment on which approximation method is better. (iii) (c) Given that x and y depend on variables u and v according to the parametric equations X = uv y = v – u. ag Determine the partial derivatives and 9. ди (You do not need to simplify/expand your answer.)
Question 2 Define the function g(x, y) = [4 – (x – 1)²][1 – (y – 2)²]. (a) Find the local maximum point(s) of g, showing the test you used to determine its nature. .1.. (b) (i) Determine the linear approximation, g' (x,y), of g near (-2,1). Determine the second-order Taylor approximation, g"(x,y), of g near (-2,1). (You do not need to simplify/expand the approximation formula.) (ii) Estimate the value of g at (-1.9, 1.2) using g and g'respectively. Compute the error from each approximation and comment on which approximation method is better. (iii) (c) Given that x and y depend on variables u and v according to the parametric equations X = uv y = v – u. ag Determine the partial derivatives and 9. ди (You do not need to simplify/expand your answer.)
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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![Question 2
Define the function
g(x, y) = [4 – (x – 1)²][1 – (y – 2)²].
(a)
Find the local maximum point(s) of g, showing the test you used to determine its nature.
(b)
(i)
Determine the linear approximation, g' (x, y), of g near (-2,1).
Determine the second-order Taylor approximation, g"(x,y), of g near (-2,1).
(You do not need to simplify/expand the approximation formula.)
(ii)
Estimate the value of g at (-1.9, 1.2) using g" and g'respectively. Compute
the error from each approximation and comment on which approximation
method is better.
(iii)
(c)
Given that x and y depend on variables u and v according to the parametric equations
X = uv
y = v – u.
ag
Determine the partial derivatives and .
ди
(You do not need to simplify/expand your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F067b8275-6021-4173-ae85-ba534da31118%2Fb9bb6d77-dc9b-4d40-9d6d-8c50fcc30690%2Flr2f8wah_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2
Define the function
g(x, y) = [4 – (x – 1)²][1 – (y – 2)²].
(a)
Find the local maximum point(s) of g, showing the test you used to determine its nature.
(b)
(i)
Determine the linear approximation, g' (x, y), of g near (-2,1).
Determine the second-order Taylor approximation, g"(x,y), of g near (-2,1).
(You do not need to simplify/expand the approximation formula.)
(ii)
Estimate the value of g at (-1.9, 1.2) using g" and g'respectively. Compute
the error from each approximation and comment on which approximation
method is better.
(iii)
(c)
Given that x and y depend on variables u and v according to the parametric equations
X = uv
y = v – u.
ag
Determine the partial derivatives and .
ди
(You do not need to simplify/expand your answer.)
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