please help me W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable.– 2, v,(2, 6) = 1, v:(2, 6)- 1,– 7, u¿(2, 6) = 9, v(2, 6)2)-If u(2, 6) — 3, и, (2, 6)-F.(3,2)5, and F,(3,- 9, then find the following:--W.(2, 6)W:(2, 6) =

Name: please help me W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are d
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Description: please help me W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable.– 2, v,(2, 6) = 1, v:(2, 6)- 1,– 7, u¿(2, 6) = 9, v(2, 6)2)-If u(2, 6) — 3, и, (2, 6)-F.(3,2)5, and F,(3,- 9, then find the following:--W.(2, 6)W:(2, 6) =

Answered: W(s, t) = F(u(s, t), v(s, t)), where F,…

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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please help me

W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable.
– 2, v,(2, 6) = 1, v:(2, 6)
- 1,
– 7, u¿(2, 6) = 9, v(2, 6)
2)
-
If u(2, 6) — 3, и, (2, 6)
-
F.(3,
2)
5, and F,(3,
- 9, then find the following:
-
-
W.(2, 6)
W:(2, 6) =

Expert Solution

Step 1

Consider the function of several variables

$W (s, t) = F (u (s, t), v (s, t))$

It is given that,

$\begin{array}{rcl} u (2, 6) & = & 3 \\ u_{s} (2, 6) & = & - 7 \\ u_{t} (2, 6) & = & 9 \end{array}$

And

$\begin{array}{rcl} v (2, 6) & = & - 2 \\ v_{s} (2, 6) & = & 1 \\ v_{t} (2, 6) & = & - 1 \end{array}$

And

$F_{u} (3, - 2) = - 5 F_{v} (3, - 2) = - 9$

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