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Real Analysis : Jacobian of Implicit Functions

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Independence and relations
Real Analysis
Jacobians (XXVI)

Jacobian of Implicit Functions

If lemda, mu, nu are the roots of the equation in k,

[x/(a + k)] +[y/(b + k)] + [z/(c + k)] = 1,

prove that del(x,y,z)/del(lemda,mu,nu) = -[(mu - nu)(nu - lemda)(lemda - mu)]/[(b - c)(c - a)(a - b)]

The fully formatted problem is in the attached file.

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Solution Summary

Jacobian of Implicit Functions are investigated. The solution is detailed and well presented.

Solution Preview

The equation in k can be written as

x(b + k)(c + k) + y(a + k)(c + k) + z(a + k)(b + k) = (a + k)(b + k)(c + k).

The main solution of the Posting is in the attached file.

Real Analysis
Jacobians (XXVI)

By:- Thokchom Sarojkumar Sinha

If are the roots of the equation in ,
,

prove that

Solution:- The equation in can be written as

...

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  • BSc, Manipur University
  • MSc, Kanpur University
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