39. Let G be the inverse of the map F(x, y)= (xy,x²y) from the xy-plane to the uv-plane. Let D be the domain in Figure 18. Show, by applying the Change of Variables Formula to the inverse G = F-', that 20 40 " dx dy = e"v-!dv du exy and evaluate this result. Hint: See Example 8. y 20 .ху 20 10- x²y = 40 x²y = 20 ху — 10- 1 2 3 4 5 FIGURE 18

Q: Let D. be the linear transformation fromc (a, 6] into cla, e). Find the preimage of the function.…

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Q: +++++ ++ + 2 riecononi ni bilw no elV us led (Jq 1) () ++++ dordw go alnoji vas da 1 (1g 1) (b) YOe…

A: follow next step

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A: We will draw the arrow diagram for function mapping from set A to set B.

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A: Given : f(x,y)=|x|+sin(y)   To sketch : contour using the k-values k=1,2,3

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: F. dr Evaluate So

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Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf.,…

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Q: Question 6 of 10 Sketch the domain of f(x, y) = Vr +y? - 4. Use solid lines for portions of the…

A: We to sketch the graph of domain

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Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: Let f(2)= iz³ + cos(z²) z² +1 i. Find f'(z). ii. Evaluate ƒ'(–2i) and simplify. iii. State the…

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Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

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Q: %24 1. コト GIPTA Let y be delined implicitly by the following equati function ofXand 2 etz sim (TX2)…

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Q: 87; Let flxiy,2) =% Cos(Tx) + kon (s2). Then find the directional derivative of f the point…

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Q: Let D = (a) § D. ds (b) , V. Ddv over the region defined by 0 ≤ p ≤ 5, -1 ≤z ≤ 1,0 < < 2. 2pz²a + p…

A: Given Information:Field: Range of each variables:To find:a)  b) Concept used:Flux of any field…

Q: Find fyzy. 9,8 f(x, y) = x°y³ – 8x*y + x f yry yxY ||

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Q: 1 use that transformations e Jaco Je √y=0 p√x=0 %cty octy=u dy dx = e = 1 2 and your to prove

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Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: 5. Calculate the divergence of F = (7x², 9y, -52).

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Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )…

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Q: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of L?

A: Suppose ABC- &gt; LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of…

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Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: Show that if (x.g) m. is re<rz, it is 8lx,r) C Blx,g) for x Ex. U.

A: Metric or Distance: A metric or distance is a function ρ :X×X→ℝ such that ρx, y represents the…