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(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.

(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.

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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(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y-z-1=0, g(x, y, z) = x + y² +2³ 2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
Transcribed Image Text:(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y-z-1=0, g(x, y, z) = x + y² +2³ 2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
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