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xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere fi(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (2₂) (1₂). Use the Chain Rule to calculate (FoG)'(x) for the various choices of x: = (-₁²) (b) x = (3) (c) x = (a) x = () (d) x = = (-¹). 21 X₂ (2y1+342) y² + y² and_G(y) = (² For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R² to R: x1 (i) fi := x² + x² - 2 (ii) f₂ | := 4x+1 X₂ := 9(x₁ - 1)² + (2+1)²-2 (iv) f₁ 21 X₂ I1 I₂. := √(x₁ + 1)² + (x₂ - 2)²

xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere fi(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (2₂) (1₂). Use the Chain Rule to calculate (FoG)'(x) for the various choices of x: = (-₁²) (b) x = (3) (c) x = (a) x = () (d) x = = (-¹). 21 X₂ (2y1+342) y² + y² and_G(y) = (² For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R² to R: x1 (i) fi := x² + x² - 2 (ii) f₂ | := 4x+1 X₂ := 9(x₁ - 1)² + (2+1)²-2 (iv) f₁ 21 X₂ I1 I₂. := √(x₁ + 1)² + (x₂ - 2)²

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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Exercise II.2. let F(.) : R² → R³ and G(): R² → R² be given by (fi(x)) f2(x) f3(x)) y = 9/₁ F(x) = where f1(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (a) x = and G(y) = (2y1 + 3y2 y² + y² 21 I₂ Use the Chain Rule to calculate (FG)'(x) for the various choices of x: - (₁²) (b) x = - (-³₁) (c) x = - (4) (d) x = For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R2 to R: (i) f₁ (22) := x² + x² − 2 = 4x² + (iii) f3 (ii) f₂ := = 9(x₁ − 1)² + (²+¹)² — 2 (iv) fa x1 X2 (=-¹). I1 In x1 X₂ and −1 == ((x₁ + 1)² + (x₂ −2)²
Transcribed Image Text:Exercise II.2. let F(.) : R² → R³ and G(): R² → R² be given by (fi(x)) f2(x) f3(x)) y = 9/₁ F(x) = where f1(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (a) x = and G(y) = (2y1 + 3y2 y² + y² 21 I₂ Use the Chain Rule to calculate (FG)'(x) for the various choices of x: - (₁²) (b) x = - (-³₁) (c) x = - (4) (d) x = For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R2 to R: (i) f₁ (22) := x² + x² − 2 = 4x² + (iii) f3 (ii) f₂ := = 9(x₁ − 1)² + (²+¹)² — 2 (iv) fa x1 X2 (=-¹). I1 In x1 X₂ and −1 == ((x₁ + 1)² + (x₂ −2)²
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