Show that Si2 f dæ + g dy + h dz = S - (4xy³z*dx + 6y?x?z4dy + 8z°y³x²dz) is independent of path: (-1,-5,-3) J(5,–1,2) c(-1,–5,-3) _ J(5,–1,2) ah -242,2,3 %3D ag az af %3D az –16xp3_3 ah |- 16xy3,3 -12y-4 ag Therefore curlF = C-1,-5,-3) Ss,-1,2)- (4xy*zªdx + 6y²x²z*dy+ 82°y%x*dz) = |

Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: Use the chain rule and compute if z = x2 + xy³, x = uv? + w°y = u+ ve" O A. = (2x + y*)(2uv) +…

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Q: 11. Find F. dr where F(x, y) = (3y, -2x) and C is the path starting at (0,0) to (4,0) to (4,4) back…

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Q: 8. Evaluate •S.F.d F-dr where F(x, y, z) = (-7 sin(7x)-yz, π cos(ny)-xz, -xy) and C is any path that…

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Q: 12. Let F(x, y) = (sin(y)), and let P represent the path that goes in straight lines from (1, 0) to…

A: We see,        = (ysin(xy), xsin(xy))        = (dx, dy) Hence,     = (ysin(xy), xsin(xy)).(dx, dy)…

Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

A: Given path is:

Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az…

A: We have to find   dz and delta z and compare the the values.

Q: Let R be the set of real numbers and d: R x R R be defined as follows. d(x, y) = 3|x - y®I. Then (R,…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0),…

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Q: (0) X. 人セこトン (242) 27 vay 4th 15 where Cis the path from P(0,0 to evaluate つlxe し use Green's…

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Q: I am having trouble with this problem

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Q: Evaluate S2xyzdx + x²zdy + x²ydz over the path c(t) = (t², sin(πt/4), et²-2t) for 0 ≤ t ≤ 2. help…

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Q: Determines the distance between the left right.

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: 3) Evaluate f.(y + z)dx + (x + z)dy + (x + y)dz, C consists of line segments from (0,0,0) to…

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Q: — X2 - 4х +

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Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

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Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

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Q: Iculate | y?dx – yz²dy – sen(z)dz, where Cis the path connecting the point A(-2, 2, 4)to the point…

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Q: Let u = u(x, y, z.) be determined near (1, 1, 1) by x²y³z²u³ + 2xy²u³ - 3x³z²u=0, u(1,1,1) = 1. Find…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: 26. Let F(x, y) = (3x + y, a?y) and let C be the path along ry = 2 from (1, 2) to (2, 1). Calculate…

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Q: 2.2 Determine whether A. dl between points p₁ (0,0,0) and p2(1,1,1) is path dependent for A = xy² +…

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Q: Use Yule-Walker equations to determine the autocovariance function of a stationary ARMA(2,1)…

A: The autoregressive models for the time series are used for their simplicity and applicability to the…

Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

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Q: he curve y = X fc (vî (yi

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Q: 8. Iff₁=e¹x,f₂=e³x and fi,f2 and f3 are linearly dependent, the f3 could be (A) sin(3x) (B) ex (C) e…

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Q: y =c,J,(x) +c_Y, (x) .A y=c,J,(x) +c,Y, (y) .B y=c,,(x)+c_y,(x) .C y=c,J,(y) +c_Yn(x)

A: Thanks for the question :)And your upvote will be really appreciable ;)