Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0

Q: Find fr and fy- ray f(r, v) = [" 3e 3e" dt f„(x, y) = fy(x, y)

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Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

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Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

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Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: 2)Evaluate || dA ,Ris bounded by y = x2 ,y = 1 et2 R. 3)Evaluate | Vy2 + 1dA, Ris bounded by x = 4-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: ƏF Find at (x, y) = (T, 1) if f (x,y) = cos vt dt. cos yt dt. ww

A: given,          fx,y=∫0x2ycostdt

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: bounded by Y=x3, V=1x i rotare about X=1

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Q: Prove that the function f : R? → R, f(x, y) = sin(/x² +|sin y|) is uniformly continuous on R?.

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: find a potential function for F or determine that F is not conservative. F=(z,x,y)

A: F is conservative when curl F = 0 Given that f=(z, x, y)=zi+xj+yk

Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: The joint pdf of a two-dimensional RV (X, Y) is given by f(x, y) = xy² + 0Sx 1), P (Y < –),

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Q: Integrate F(x, y, z) = z - x, over the cone z = sqrt(x2 + y2), 0&lt;= z &lt;=1

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: (B) Find the potential function V = V(r, y) such that %3D + yi+ + r)j = V¥ 1+ x2 + y? 1+ x? + y? and…

A: We have to find the potential function ψ=ψx,y such that x1+x2+y2+yi+y1+x2+y2+xj=∇ψ and also evaluate…

Q: Assume that X and Y have joint pdf Sr + 3x?y if 0 <r<1 and 0 < y < 1, f(x, y) = %3! otherwise.

A: We know that, Covariance(X,Y) = E(X).E(Y) - E(XY) Here E(X) and E(Y) are given so we'll Calculate…

Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

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Q: Evaluate / f(z)dz when ) f(z) z+1 and y = TR (R > 0) z2 (ii) f(z) = (z+1)³ sin(z2022) and y = r(0;…

A: Given function i fz=z+1z2 and γ=ΓRR&gt;0iifz=z+15sinz2022 and γ=γ0;1

Q: At what points (x, y, z) in space are the functions in continuous? ƒ(x, y, z) = x2 + y2 - 2z2

A: Solution:-  At what points (x, y, z) in space are the functions in continuous? Let (m,n,p) is the…

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: Determine the vactor feld of F. F(z, y) = yi - j

A: This is a problem related to vector field calculation. Based on the general concept we will provide…

Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Let F(x,y,z) = z* + x+ y sin x + x In z 0, where z fx.y), then at (0,0,1) and are dy equal to: ax

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Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

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Q: b) f(x): 1 + sec2

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Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

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Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: Evaluate the divergence of F = (exy, xy, z4) at P = (l, 0, 2).

A: Given  F=exy, xy,z4 at P=1,0,2

Q: F(x, y, z) = xyzi+ (2ry+2) j+y°z°k conservative?

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Q: Find f, for f(x, y) = | cos(r*) dt.

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Q: . Assume that f(x, y) is continuous on [a, b) x [c, d] and 9(r, v) = | 5(6,t)dt ds for a <a < b, c <…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: Find fr and fy- f(x, y) = ets dt %3D f (x, y) = %3D fy(r, y) =

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Q: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…