Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x- 5y)i + (5x- 4y)j C: The circle (x- 3)² + (y – 3)? = 9

Q: Find the points on the curve a = t – 16t + 1, y = t² + 12t – 8 that have: %3D A. a horizontal…

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Q: r(t) = ti + (2tt2) intersect the paraboloid (2) At what points does the curve r(t) z = x² + y²?

A: We are asked to find the intersection point.

Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

Q: Consider the following. x = t³, y = In(t) X = (a) Eliminate the parameter to find a Cartesian…

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Q: Find an equation of the plane tangent to the following surface at the given point. z=6-3x- 3y; (2,3,…

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Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

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Q: Find the length of the curve C defined parametrically by C: 2(t) = e'cost, v(t) = e'sint, 0SISR…

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Q: At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter…

A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

Q: Sketch the plane curve r(t) = 3ti − tj and find its length over the given interval [0, 3] .

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Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

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Q: Find the equation of the tangent plane to the surface z=9x^5+2y^5+1xy at the point (0,−1,−2) z=

A: From tangent plane equation to a curve

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: At what points does the curve  r(t) = ti + (5t − t2)k  intersect the paraboloid  z = x2 + y2

A: We have to find the intersection point

Q: Sketch the plane curve r(t) = t3i + t2j and find its length over the given interval [0, 1] .

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Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

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Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

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

Q: Find an equation of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: Find an equation of the tangent plane to the surface 4x^2 + 9y^2 − z^2 = 14 at P = (2, 1, 4).

A: Given,4x2+9y2-z2=14at P=(2,1,4)

Q: Find the equation of the tangent plane to the surface z = + y? x2 4 at the point (2, -2, 5) x- 4y -…

A: We have to solve

Q: The curve r+y-6x2y 0 is symmetric about Oy = 0 Ox = 0 Oy =x None of these

A: We need to check the symmetry of the curve x4+y3-6x2y=0

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: At which of the points below is the tangent plane to the surface - 2y² + z²+ yz = 2 vertical? Select…

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Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0,…

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Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Find the equation of the plane tangent to the following surface at the given points. 2 x +y -z - 52…

A: See the details solution in below

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

Q: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

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Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

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Q: Find an equation of the plane tangent to the following surface at the given point. z= 3- 3x -y:…

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

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Q: If C denotes the curve parametrized by x = t, y = 2t2, z=t°, 0 <t < 1, then fx dz +y dy + z dx C O…

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Q: determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.

A: Curve will have critical point if it have vertical tangent or horizontal tangent . Slope of…

Q: Find the length of the curve C defined parametrically by C: r(t) = y(t) = e' sin t, 0<t<n e cost,…

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Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x2 + y2? (If an…

A: knlk

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

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Q: Let y(t) = (1/2)te*/2, 0<t< 2n What is the terminal point of the curve? — 2п

A: Terminal point of curve is obtained at terminal point of path.

Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.