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Question 4 Consider functions lano (iog 02) a ald h(u, v) = (h1(u, v), h2(u, v)) : R² → R².ag d) () f(x, y) : R2 →R and %3D Below is a table of different values of various objects related to these functions. f(2,-3) = 5 of(2,-3 (2,-3) =0 af -(2,-3) =0 (2, 2,-3) =1 a (2, –3) = 4 azây -(2,-3) = -1 af -(1, –1) =3 (1,-1) =-1 Ou (1,-1) = -3 -(1,–1) = 2 azdy f(1, –1) = 3 Əz (1, –1) =0 ahi (2,-3) = 3 dv ) (d) (2,-3) = 1 h1 (2, –3) = 1 (2,-3) =1 ôu? (2, -3) = 1 dn2 (2, -3) = 9 ahi h2 (2,-3) = 14 ahi (2,-3) =2 (2,-3) =7 dv (2,-3) = 1 -(2,-3) = 1 %3D h2(2,-3) = -1 a) Compute the second order Taylor approximation T2(h1, h2) of the function f at (1,–1). :( noit (e) (e bojure) U B)Identify a critical point of f and determine if it is a local max, local min or a saddle point. dt lo inolharg ods lo suil wo a (12, -(aco) 0 diq d l (aioq &) (b) ont saneL art TeT+ C) Use the chain rule to compute D(f o h)(2, –3).

Question 4 Consider functions lano (iog 02) a ald h(u, v) = (h1(u, v), h2(u, v)) : R² → R².ag d) () f(x, y) : R2 →R and %3D Below is a table of different values of various objects related to these functions. f(2,-3) = 5 of(2,-3 (2,-3) =0 af -(2,-3) =0 (2, 2,-3) =1 a (2, –3) = 4 azây -(2,-3) = -1 af -(1, –1) =3 (1,-1) =-1 Ou (1,-1) = -3 -(1,–1) = 2 azdy f(1, –1) = 3 Əz (1, –1) =0 ahi (2,-3) = 3 dv ) (d) (2,-3) = 1 h1 (2, –3) = 1 (2,-3) =1 ôu? (2, -3) = 1 dn2 (2, -3) = 9 ahi h2 (2,-3) = 14 ahi (2,-3) =2 (2,-3) =7 dv (2,-3) = 1 -(2,-3) = 1 %3D h2(2,-3) = -1 a) Compute the second order Taylor approximation T2(h1, h2) of the function f at (1,–1). :( noit (e) (e bojure) U B)Identify a critical point of f and determine if it is a local max, local min or a saddle point. dt lo inolharg ods lo suil wo a (12, -(aco) 0 diq d l (aioq &) (b) ont saneL art TeT+ C) Use the chain rule to compute D(f o h)(2, –3).

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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Question 4 Consider functions nd bleno (niog 0) a avaldo h(u, v) = (h1(u, v), h2(u, v)) : R² →R².iog d) (n) Below is a table of different values of various objects related to these functions. f(x, y) : R² → R and f(2, –3) = 5 dz (2, -3) = 0 (2, –3) = 0 a2 (2, –3) = 1 u (2, –3) = 4 fie Əzôy (2, -3) = –1 f(1,–1) = 3 (1, –1) = 3 af a, (1, –1) = -1 ar2 (1, –1) = 0 du2 (1, –1) = -3 azəy 1,-1) = 2 h1 (2, –3) = 1 (2,-3) =1 ah (2,-3) = 3 a) (d) du2 (2, -3) =1 Fuż (2, –3) = 9 (2,-3) = 1 h2(2, –3) = -1 -(2,-3) =2 (2,-3) =7 (2, -3) = 14 du2 (2,-3) = 1 h2 duôn (2, -3) =1 a) Compute the second order Taylor approximation T2(h1, h2) of the function f at (1, –1). oitat a dale oso 2son (iniog a) () B)Identify a critical point of f and determine if it is a local max, local min or a saddle point. odt lo inolbarg ods lo suil wo a (+ -()co) 0b dinq od sl (ahiog ) (b) c) Use the chain rule to compute D(f o h)(2, –3).
Transcribed Image Text:Question 4 Consider functions nd bleno (niog 0) a avaldo h(u, v) = (h1(u, v), h2(u, v)) : R² →R².iog d) (n) Below is a table of different values of various objects related to these functions. f(x, y) : R² → R and f(2, –3) = 5 dz (2, -3) = 0 (2, –3) = 0 a2 (2, –3) = 1 u (2, –3) = 4 fie Əzôy (2, -3) = –1 f(1,–1) = 3 (1, –1) = 3 af a, (1, –1) = -1 ar2 (1, –1) = 0 du2 (1, –1) = -3 azəy 1,-1) = 2 h1 (2, –3) = 1 (2,-3) =1 ah (2,-3) = 3 a) (d) du2 (2, -3) =1 Fuż (2, –3) = 9 (2,-3) = 1 h2(2, –3) = -1 -(2,-3) =2 (2,-3) =7 (2, -3) = 14 du2 (2,-3) = 1 h2 duôn (2, -3) =1 a) Compute the second order Taylor approximation T2(h1, h2) of the function f at (1, –1). oitat a dale oso 2son (iniog a) () B)Identify a critical point of f and determine if it is a local max, local min or a saddle point. odt lo inolbarg ods lo suil wo a (+ -()co) 0b dinq od sl (ahiog ) (b) c) Use the chain rule to compute D(f o h)(2, –3).
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