Let f(x, y) = x²y – xy. Evaluate | Vf•dr where C is any oriented curve from (4, –1) to (1,5).

Q: Evaluate |F. dR, where F(x,y, z) = (x, – 2, y) and C' is the curve given by R(t) = (2t, 3t, –t2), 0…

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Q: Let C be the parametric curve defined by Sx(t) = t² - 2, y(t) = t³ - 3t + 1. Determine if C is…

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Q: B) Evaluate the line integral F-dr, where F (x, y) = r*y°i+x²y°j and C is the curve r (t) = (t³ +…

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Q: Evaluate f. x'dz +z?dy +y?dx where C is the curve x = t ,y = t2, z = t? from t = 0 to t = 2.

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Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x -…

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Q: Evaluate S. x?dz + z?dy + y?dx where C is the curve x = t2 ,y = t², z = t² from t = 0 to t = 2.

A: We will use concept of line integral to solve this.

Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

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Q: Show that this curve y represents the vector (1,0) as v = 1- +0- in the sense that, for an arbitrary…

A: Given that γ(t)=(t,t2)in R2, t∈[-1,1] The objective is to show that curve represents the vector…

Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j + 9k, 0 < t s…

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Q: Find the work done by F = - 2zi + 7xj + 5yk over the curve C in the direction of increasing t. C:…

A: Solution of this question is

Q: Evaluate the line integral F dr where F (x,y) - xy'i+ yj and the curve C is the shortest path from…

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Q: s Compute yz dz + zzdy + zydz along the curve (t, t2, t³), 0 st<1

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Q: Let f(x, y) = 2xy – 4x² + 3y². %3D Then a standard equation for the tangent plane to the graph of f…

A: The function is given. Find the partial derivative fx and fy at the given point. Given,…

Q: Compute f ds for the curve specified. f(x, y, z) = xz, r(t) = (3e, 2v5t, 4e) for 0sts 1

A: Here the provided function f(x, y, z) of three variable and a curve C is defined. Then the line…

Q: Let C be the parametric curve defined by Sx(t) = t2 – t – 2, |v(t) = t* – º +t. Determine if C is…

A: Substitute x=-2 in the given equation xt=t2-t-2 and simplify to calculate the value of t.…

Q: Calculate . F · dr where F (x, y, z) = zi + xyj - y?k On the curve C r(t) = t?i + tj + vĩ k, 0<t <1…

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Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t2j+ 9k, 0 <ts v7.…

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Q: B) Evaluate the line integral F-dr. where F (x, y) = x*y²i+x²y°j and C is the curve r (t) = (t³ +…

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Q: Find the work done by F = xyi+yj - yzk over the curve r(t) = ti + t²j + tk, 0≤t≤1

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Q: 6. (a) Show that F = (3a²y+2, x3 + 3) is conservative. (b) Evaluate Sc(3x²y +2)dx + (x³ + 3)dy where…

A: According to the problem, we have

Q: Consider F and C below. F(x, y, z) = (y²z + 2XZ² ) Î + (2xyz)j + (xy² + 2x² Z) K₂ C² X=√E, y = t +…

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Q: 5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

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Q: Evaluate F ds (or F ds) where Jc F = (y – x2, z - y², x – z) and C is the curve r = joining (0,0,0)…

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Q: Consider the curver (t) = (t, t³, tº); t > 0 Find an equation for the projection of the curve on xy…

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Q: Let G(x. y)=x*yi+(y+xy*)j. Evaluate the line integral [G-dr, where Cis the curve x= ť and y=t* for…

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Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

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Q: Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: Since you have posted multiple questions according to company policy we are supposed to be answer…

Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: Let C be the parametric curve defined by x(t) = t² – 2, y(t) = t³ – 3t + 1. Determine if C is…

A: Given that,A parametric curve C is defined byx(t)=t2-2y(t)=t3-3t+1The concavity of the parametric…

Q: Compute / f ds over the curve specified. (1) f(x, y, z) = z², r(t) = for 0 < t < 2

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Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 sts 2

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Q: Determine the torsion at t = 0 of a curve a : [−1, 1] → R3, a(t) = (2t, t^2, t^3/3). Moreover,

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Q: Let C2 be the curve defined by R(t) = (t² +t + 3, 4t – 5, 2+ t – t2), t e [0, 1]. %3D | (x + y+ 2)…

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Q: Let C: [o,2]> R be a curve defined by C(t) = (t²,t'). Evaluate. Sy dx x dy.

A: Given:  C: [0, 2]→ℝ2   is a curve defined by                C(t)=(t2, t3)implies x=t2 and…

Q: Evaluate f, x*dz + z*dy + y*dx where C is the curve x = t,y = t, z = t? from t= 0 to t= 2.

A: x = t2 ,  y=t2, z=t2 dx = 2t dt,  dy= 2t dt, dz = 2t dt  Putting values in the integral: ∫02t4(2t…

Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

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Q: Let C be the curve connecting (0,0) to (1,2) to (0,6) to (0,0) using straight lines. (5x*y – 3x²y+…

A: Greens theorem based problem......

Q: 1. Compute (1/zy, 1/(z + y))- dr along the curve (t, t2). 1<ts4

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Q: IF=(x+y)i+(y– )j+z?k over the curve r(t) = (t²,t²,t*), 0sts1

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Q: 3. If Ø = 2xyz?,F = xyî – zĵ + x²k and C is the %3D curve x = t2, y = 2t, z = t³from t = 0 to t = %D…

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Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

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Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

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Q: Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and…

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Q: Find the tangent plane to f(1, y) = ar² + 5y² + 71²y² +9x +5y at the point (3, 6). %3D

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Q: Evaluate c (xy + y + z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0st<1.

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