Let u and v be defined implicitly as functions of x and y by the equations xv + yu 5 x² – y3 + uv² = 2 (a) Show that u and v can be expressed as unique C' functions of x and y near (x, y, u, v) : (3, 2, 1, 1). (b) Compute ди at (x, у, и, v) — (3, 2, 1, 1).

Let u and v be defined implicitly as functions of x and y by the equations xv + yu 5 x² – y3 + uv² = 2 (a) Show that u and v can be expressed as unique C' functions of x and y near (x, y, u, v) : (3, 2, 1, 1). (b) Compute ди at (x, у, и, v) — (3, 2, 1, 1).

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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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Let u and v be defined implicitly as functions of x and y by the equations
xv + yu
5
x² – y3 + uv² = 2
(a) Show that u and v can be expressed as unique C' functions of x and y near (x, y, u, v) :
(3, 2, 1, 1).
(b) Compute
ди
at (x, у, и, v) — (3, 2, 1, 1).

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