5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: 1. Let T = [-2 1 0 5], 5 1 1 0 A = [¦ ¦] ·--[¦ ¦ ). -- [¦ ¦ ¦]. - -[] [16], B = = [1 2] C = D = 0 3…

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Q: 1. 다음에서 u.v를 구하여라. (4) u (7, 6, 2) v (3, 1, 2) s (1) u = (4, 7,-1) v = (-2, 1, 4) (2) u = (-1, -2,…

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Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: Find the following. = ( ₁₁ — 1) , V₁ 1, = 2 U = (a) ||u|| (b) (c) ||u + v|| (d) (e) ||v|| (f) — 33 u…

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: Calculate 7 af Әх af af af af 7 Әх ду Әх af ах af ду (1, -1) (1, -1) f(x, y) = x4y3 - х = = = , and…

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Q: The Doman off(x) = V4 – Vx is

A: Note: The correct option is not in the option.

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(3, 6) = -7, us (3,- 6) =…

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Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: 4. [p^ (q v-r)] →→(~p^q) STT P T T TFFFF ... LTTFFTTEF 9 r LTFTFTFIE Т Т qv-r p^(qver) P ~p ^q…

A: The given statement p∧q∨~r→~p∧q. We have to construct a truth table for the statement.

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 2 f(x,у) 3 V9- х* -Зу;B Р(3, - 3); 13 3 13

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Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: 2 [11]₁v=₁-1²] W u Compute: u.v= u. W = w u · (v + w) = u.v+u. W =

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Q: 1. Given f(x, y) = x' + y* find and ax?' dy' axðy дудх 2. Find whether the function F = (r² – y' )i…

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: f(x,y) af ?x af ду = af ду X 2x² + 8y² f(x, y) = tan af ?x (5)

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Q: For the function of two variables defined by f(u, v) = u cos v + v² sin u, select the option that…

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Q: If F(u, v) = u³ ln(2v) and u = x - 2y, v = " y compute 8² F Әхду

A: We need to find derivative of function F with respect to x and y.

Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: Let z = f(st – 3, s? +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: 2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t…

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Q: z = f(st – 3, s+t°) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = fz(-1,9) = 2.…

A: (b) Apply the chain rule, ∂z∂t=∂f∂x×∂x∂t+∂f∂y×∂y∂tNow differentiate partially with respect to…

Q: For f(x.y) = 3x* - 4x°y+5y° - 4, find f,(1, – 2). O A. 12 О В. - 12 OC. 36 O D. 24

A: