Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2, –1,2) to B = (1, –1,3).

Q: 7x – 4xy = C

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Q: Let F(x, y) = xy + 2y² + 20x – 4y – 33. Find all values of ysuch that F(y, y) = 2.

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Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

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Q: Q1. If g = xy - yz - · — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F…

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Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: Find fy fy and f, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz – 7yz, (-2, 1, 2)

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: iv) if zx = (y)¯1 then zx/Zy %3D

A: We have to find          zxzy where , zx=(y)-1 If ,   z=z(x,y)  then,∂z∂x= derivative of z with…

Q: Find the soln of the ff: U.E a) y - 3y'tɔy = ei yo=Y'o) =0 4 Xt) 6) x't) - 4x) + - 4e* -4

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Q: let z(t) = f(x,y) where x=3-2t, y=t2+4 Find z'(0) if fx(3,4)= -1 and fy(3,4)= 8.

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

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Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: The linear transformation Dx:C'a,b→Ca,b maps a function fx to its derivative Dxf. Here, given that…

Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D d) – 2 e) - 4 g) None of…

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Linear transformation

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Let f(z) = kz5 + az3 + cz.  Find u(x,y) if z = 3.9 + 6.3i , a = 5, c = 10, and k = 4. Round off…

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Q: Let f(x, y) = xy+ + 2x²y + 4y5 (a) Find fr- (b) Find fy-

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Q: If f(x,y) = 3e2y cos (x-2), then the linear approximation at (2,0) is %3D (A) 3-3x (B) 3+ 6y (C)…

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Q: - Q1. If g = xy — yz — zx and F = x²y ī− 2 y²zj – z²x k, find F. grad g and cross product of F and…

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Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: Find the absolute maxima and minima of f(x, y) = 3x2 + 10y on the closed triangular region bounded…

A: Consider the equation

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: Let Dx be the linear transformation from C'[a, b] into Cla, b]. Find the preimage of the function.…

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: Q1. If g = xy — yz — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and…

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Q: Let z = f(x, y) = e**y while x = 2st and y = s² + t³. Use a chain rule to find ôz/8t at the points…

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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Q: o Find the Vf at the given point 2. (x,y.2)=(x² + y² + ²)² +In.xyz,P(-1,2,–2)

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx

Q: Is AX'Y'Z' a reflection of AXYZ across line g? g X. Z' Y X'

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