1. For each F(x, Y) = 0, find dy/dx for each of the following: (а) у - 6х + 7 0 (b) 3y+12x + 17 =0 () x? + 6x - 13 - y= 0 2. For each F(x, Y) = 0 use the implicit-function rule to find dy/dx: (a) F (x, y) = 3x2 + 2xy + 4y³ = 0 (b) F (x, y) = 12x$ - 2y = 0 (C) F(x, y) = 7x? + 2xy² + 9y = 0 (d) F(x, y) = 6x3 - 3y = 0 3. For each F(x, Y, 2) = 0 use the implicit-function rule to find ay/ax and ay/az: (a) F(x, y, 2) = x y³ + z? + xyz = 0 (b) F (x, Y, 2) = x³ z² + y³ + 4xyz= 0 () F(х, у, 2) — Зx*уз + x2?у2 + уб гх + у?z%3D0 4. Assuming that the equation F(U, x1, X2, ..., Xn) = 0 implicitly defines a utility func- tian U = f(x1, X2, . . , Xn) : (0) Find the expressions for aU/ax2, au/axn, ax3/ax2, and ax4/axn. (b) Interpret their respective economic meanings. 5. For each of the given equations F(y, x) = 0, is an implicit function y = f(x) defined around the point (y = 3, x = 1)? (а) х3 2x2у + Зху? - 22 %3D 0 (b) 2x2 + 4xy – y + 67 = 0 %3D %3D
1. For each F(x, Y) = 0, find dy/dx for each of the following: (а) у - 6х + 7 0 (b) 3y+12x + 17 =0 () x? + 6x - 13 - y= 0 2. For each F(x, Y) = 0 use the implicit-function rule to find dy/dx: (a) F (x, y) = 3x2 + 2xy + 4y³ = 0 (b) F (x, y) = 12x$ - 2y = 0 (C) F(x, y) = 7x? + 2xy² + 9y = 0 (d) F(x, y) = 6x3 - 3y = 0 3. For each F(x, Y, 2) = 0 use the implicit-function rule to find ay/ax and ay/az: (a) F(x, y, 2) = x y³ + z? + xyz = 0 (b) F (x, Y, 2) = x³ z² + y³ + 4xyz= 0 () F(х, у, 2) — Зx*уз + x2?у2 + уб гх + у?z%3D0 4. Assuming that the equation F(U, x1, X2, ..., Xn) = 0 implicitly defines a utility func- tian U = f(x1, X2, . . , Xn) : (0) Find the expressions for aU/ax2, au/axn, ax3/ax2, and ax4/axn. (b) Interpret their respective economic meanings. 5. For each of the given equations F(y, x) = 0, is an implicit function y = f(x) defined around the point (y = 3, x = 1)? (а) х3 2x2у + Зху? - 22 %3D 0 (b) 2x2 + 4xy – y + 67 = 0 %3D %3D
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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Transcribed Image Text:1. For each F(x, Y) = 0, find dy/dx for each of the following:
(а) у - 6х + 7 0
(b) 3y+12x + 17 =0
() x? + 6x - 13 - y= 0
2. For each F(x, Y) = 0 use the implicit-function rule to find dy/dx:
(a) F (x, y) = 3x2 + 2xy + 4y³ = 0
(b) F (x, y) = 12x$ - 2y = 0
(C) F(x, y) = 7x? + 2xy² + 9y = 0
(d) F(x, y) = 6x3 - 3y = 0
3. For each F(x, Y, 2) = 0 use the implicit-function rule to find ay/ax and ay/az:
(a) F(x, y, 2) = x y³ + z? + xyz = 0
(b) F (x, Y, 2) = x³ z² + y³ + 4xyz= 0
() F(х, у, 2) — Зx*уз + x2?у2 + уб гх + у?z%3D0
4. Assuming that the equation F(U, x1, X2, ..., Xn) = 0 implicitly defines a utility func-
tian U = f(x1, X2, . . , Xn) :
(0) Find the expressions for aU/ax2, au/axn, ax3/ax2, and ax4/axn.
(b) Interpret their respective economic meanings.
5. For each of the given equations F(y, x) = 0, is an implicit function y = f(x) defined
around the point (y = 3, x = 1)?
(а) х3 2x2у + Зху? - 22 %3D 0
(b) 2x2 + 4xy – y + 67 = 0
%3D
%3D
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