a- -- Find the curl of. v = (y²z₁e",x²y)

Q: x' = -x 22. Find homeomorphism H for {y = y +x³ near origin.

A: Given that  x'=-xy'=y+x3 The solution for x'=-x is x=Ae-t The solution for y'=y+e-3t is,…

Q: Find the divergence and the curl of V = zi+yj + xk.

A: find out the divergence and curl of v :  V = Z i + y j + z  k

Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

A: Given problem:-

Q: Find paromet ric aquation of Line L where to paiut A(Xmiya) is and

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Q: of ū at the poir 01

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Q: DETAILS MY NOTES LARCALC12 15.1.071. [-/4.54 Points] (V Find curl(curl F) = ▼ × (▼ × F). F(x, y, z)…

A: Step 1: Step 2: Step 3: Step 4:

Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

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Q: 2. Find a formula for curl(curl(u)) in terms of (x1,02, X3) and (e, e2, e3) if u = uje1 + Uze2 +…

A: We will use the basics of vector calculus to answer this question in detail. Below is the…

Q: 8. Which of the following is the curl of F = (2xy +1, x² + 2yz, y² – 2 )? %3D а. 0 b. 1 с. -1 d. 2

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Q: suppose that S = [a, b] x {0} is a closed line segment %3D in R?. Show that H' (S) = b a.

A: Here given as S=a, b×0 is a closed line segment in ℝ2. We have to prove that H1S=b-a

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: Find 2"dz for the case of z(= a) # z(= b), and when the curve is closed, that is when a b.

A: Note: We are not given any specification of n and the curve C. So, we have taken various cases here.…

Q: if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20…

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Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

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Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: 3. Use Green's Theorem to evaluate x² + y² = 4. (976337703) [F(r) dr where F =(2²+y³)2 + 3xy²j and C…

A: I have explained everything with in the solution. Please go through that.

Q: Use Green's Theorem to evaluate [F(r) dr с

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Q: 2. Triangle FGH with verlices F(1,8), G(5, 7), and H(2, 3): y-x F' G' H' - 177

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Q: find curl (grad Q).

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Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).

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Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: Ifu =x +y²+z², find curl Vu.

A: Solution:-

Q: Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express…

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Q: Which of the following is/are points on the curve y-x Br+ 22x - 24x +9 whore the tangent line is…

A: We need to find the points on the curve where the tangent line is parallel to the x-axis.

Q: m while the (2) Find the ualue of the constanl Curl of Fasie) = mxy.ge?) Ĉ + cm-7)xi+ (I-m)×2°R is…

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Q: „If A = 2xzi - yz} + 3xz'k then find curl (curl A) at (1, 1, 1). %3D .If o =x'yz and A = 2xz1- yzj +…

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Q: 5. Given that F = xzi– 2yzj+x²yzk Find the followings at (1, 1, 3): (a) div F. (b) curl F. (c) ▼·(V…

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Q: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

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Q: 37.Calculate the value of r such that the line x + 2 y + z = 0 is a center-line of the conic section…

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Q: Let S(x) be a natural cubic spline that passes thorugh the points (-1,1), (0,2), and (1,1). Then,…

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Q: Show that the curve In (2X-1) , n> i has no stationary point

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Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

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Q: 2=5x²- is EaJoxus Firnd an The curve 0ith equatio %3D kampyle of the Colled a equatien f at he peint…

A: Given : y2 = 5x4-x2