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Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. u(1, −9) = 3 v(1, −9) = 0 us(1, −9) = 9 vs(1, −9) = −6 ut(1, −9) = 4 vt(1, −9) = 7 Fu(3, 0) = −2 Fv(3, 0) = −4 Find Ws(1, −9) and Wt(1, −9).

Answer :

fahadisahadam

Answer:

[tex]W_{s} =6\\W_{t} =-36[/tex]

Step-by-step explanation:

               u                                       v

[tex]u(1, -9) = 3.......................v(1, -9) = 0[/tex]

[tex]us(1, -9) = 9....................vs(1, -9) = -6[/tex]

[tex]ut(1, -9) = 4.......................vt(1, -9) = 7[/tex]

[tex]Fu(3, 0) = -2.....................Fv(3, 0) = -4[/tex]

To find [tex]W_{s}[/tex]

Now we can apply the above expression

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

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

         =([tex]F_{u}[/tex](3, 0), [tex]F_{v}[/tex](3, 0)) · (9, -6)

        [tex]=(-2,-4).(9,-6)\\=(-18)+(24)\\=6[/tex]

To find [tex]W_{t}[/tex]:

(1,-9)=((u(1, -9), v(1, -9)), (u(1, -9), v(1, -9))) · ((1, -9), (1, -9))

          = ([tex]F_{u}[/tex](3, 0), [tex]F_{v}[/tex](3, 0)) · (4, 7)

          [tex]=(-2,-4).(4,7)\\=(-8)+(-28)\\=-36[/tex]

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