Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure 14,0,01

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

Q: (2) Evaluate S. 2 - xy ds where C is the upper half of the circle centered at the origin of radius 1…

A: Evaluate.

Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

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Q: Exercise (2): Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: We have to find the line integral

Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: 6. Set up but do NOT evaluate Evaluate the line integral 2 curve (t) - (t", t), where 0sts0. L ds,…

A: Consider the given integral as ∫Cyxds, where C is the curve r⇀t=t4,t3 and 0≤t≤1. Note that, the line…

Q: 2) Evaluate the vategral if cis any Seetion al Smooth Curve from 10,0,0) to (lilil). .(-3p²+2y-Z) da…

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Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)

A: We have to find the equation of  tangent plane.

Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

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Q: 6. Evaluate the line integral g. x²y² dx + xy dy where C consists of the arc of the parabola y = x²…

A: (a) Direct method The given line integral is ∮C x2 y2 dx + xy dy. The curve C consists of    C1 :…

Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many…

A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Find an equation of the normal line to the surface given implicitly by z = sin(xy) at the point…

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Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: At a certain moment, a moving particle has velocity v = (2, 2, −1)and a = (0, 4, 3). Find T, N, and…

A: Given: At a certain moment, a moving particle has velocity v = (2, 2, −1) and a = (0, 4, 3)  Now we…

Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Given ellipse with centers at (0,0) and two vertices (1,0) and (-1,0).

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: 1. Evaluate S. (2x+ y² – z) ds where C is the piecewise smooth curve below. (0, 1, 1) (0, 0, 0). (0,…

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Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Exercise 1.3.2 Give a paramatrization for the curve curve y = x³ + ()x-¹, then deduce the length of…

A: Given curve is  y=16x3+12x-1

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: The scalar path integral 3(16-a y-) ds, where the path C is the straight line from the point (0,0)…

A: This is a problem of line integral. Since the path given for line integral is embedded on the x…

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

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Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

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Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

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Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: about the line x = -2 ソ=2× ソ=2° 1 2

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Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: (6) Evaluate the line integral / r²ydx + xy°dy, where C is the square with vertices (0,0), (1,0),…

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Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: 3. Show that the line integral | (r + y)dx + xdy is independent of path and evaluate this integral…

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: 1) The plane of 2 = x*+y² X+y+2 = 12 and %3D inter sect along d para boloid Find the curve. lowest…

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Q: 2. Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xyax - (4y + 2x2)a, + 8zaz. Use…

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Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

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Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

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Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).

A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…