42-46 Find a vector function that represents the curve of intersection of the two surfaces. 42. The cylinder x + y² = 4 and the surface z = xy %3D 43. The cone z = /x² + y? and the plane z = 1 + y 44. The paraboloid z = 4x² + y² and the parabolic cylinder y = x

Q: 1. Use the parameter r =t to find a vector-valued function for the space curve represented by the…

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Q: a) Start by finding a single vector function that represents the intersection of the surfaces z =…

A: (a) Given that: Start by finding a single vector function that represents the intersection of the…

Q: 3. (a) Show that the two surfaces S1 : z = xy and S2 : z =3x^2/4 - y^2 perpendicularly at the point…

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: Let C be the curve of intersection of the paraboloid a² + y² = z and the cylinder +(y-1)² = 1 (a)…

A: Given that C is the curve of intersection of the paraboloid x2 + y2 = z and the cylinder x24 + y -…

Q: 41. The cone z = /x² + y² and the plane z = 1 + y

A: Solution: The objective is to find a vector function that represents the curve of intersection of…

Q: 3. Let C be the circle x + y = 16 and let S be any surface above the xy-plane with C as its…

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Q: A vector normal to the surface y-:=3 at the point (-1-2, 2) is (a) i+2j+k (b) -i+j+2k) (c) (21 -j+k)…

A: Definition used -              For finding a normal vector to the given surface, We have to find…

Q: Consider The curve of intersection of the parabolic cylinders x = y? and z = x?. Find an equation of…

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Q: Verify Stoke's theorem for the vector point function yz2 (xz² .3 + ex over the surface S of the cube…

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Q: r(t) = (x(t), y(t), z(t)) where x(t) = – 4t2 – 5t – 3 y(t) = 5t² + 5t +3 z(t) = – 5t? - | '(t) =…

A: Here, we need to find the binormal vector B. We are given that r(t)=<x(t), y(t), z(t)> where…

Q: 4 (2). Consider the surface S of equation z = An equation for the tangent line to S at the p(2.1.2).…

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Q: Find a vector valued function which gives the curve of intersection of  y2 + z2 =16  with the plane…

A: Given the curves:

Q: Q2/ find the parametic equation for the line passi through the pont (o,1,2) that is parallel to the…

A: To find parametric equation

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Q#1 Evaluate ſ,A.n ds , where A = z i+ xj-3y°z k ( i, j, k are unit vectors) and S is the surface of…

A: Let ∅=x2+y2-16  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: r(t) = (x(t), y(t), z(t)) where = -2t? + 3t + 3 æ(t) y(t) = 2t – 2 = 2t? + 5t = - z(t) || Since all…

A: Given vector rt=xt, yt, zt where xt=-2t2+3t+3yt=2t-2zt=2t2+5t We need to find the binormal vector Bt

Q: Given that, f(x, y) = 11 − (x − 2)^2 − (y + 4)^2 1)Determine the domain and range of this…

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Q: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter in your…

A: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter

Q: 19. Supposethat the normalunit vector N of a surface S at z = f(x,y) is determined, how does the…

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

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Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: YouTrylt 4 Find a vector function r(t) that parameterizes the intersection of the elliptic cyl 9 4…

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Q: 8. Let f(x, y)=cos(3x+2y). a. Find the minimum value of the directional derivative for f(x,y) at the…

A: We have to find  find the minimum value of the directional derivative for f(x, y) at the given…

Q: The curve of the vector function r(f) =/3 costi-2sintj, 0<t<2T is the ellipse 3 x² y? = 1 4 2y2 the…

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Q: Consider the curve r(t) that represents the intersection of the surfaces x -4z´ – 2x – 16z –19=0 and…

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Q: 5. Find the rate of change of f(x, y) = x² + y² at the point (1, 2) in the direction of the vector u…

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Q: x² + y? Find a vector function that represents the curve of intersection of the paraboloid z = and…

A: Given curves are the paraboloid z=x2+y2 and the cylinder x2+y2=4

Q: 2. Consider curve C at R whose parameterization is given by: 3t + 3 r(t) = (t + 1, ,-t? - 2t + 3)…

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Q: O Solve the electric flux through a paraboloid z =x² + y² – 16 that lies below plane z = 0. It is…

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Q: 6. (a) Show that the curve represented by the vector function F(t) = (5t, 3t – 4, 2t² – 6) is at the…

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Q: Calculate the work done by the force F= y^3(y over 3).i + x^3(x over3).j  along the displacement…

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Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

A: TO solve the question, we use the following facts (a) A functions is differentiable at a point if…

Q: Given r(t) be the vector function that describes the curve of intersection between the cylinder…

A: First, parametrize the cylinder equation to get x(t) and y(t) and then find find z(t) from the…

Q: 2. Consider the ellipse x2 y? +. 4 1 - a. Describe this curve with a vector valued function r(t), 0…

A: We have to find vector valued function and tangent vector at point t=π4.

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

Q: Usé the parameter x = t to find a vector-valued function for the space curve represented by the…

A:

Q: implement Stokes ' Iheorem by taking the vector function A = (x² + z)i + (y² + x)j + (z² + y)k on…

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Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1…

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Q: 1) Find a vector function r(t) that represents the intersection of the surfaces: = /x² + y² z = y +…

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Q: Let ƒ(x,y) = x²e"9. Give the unit vector that points in the direction of maximum increase along the…

A: Given that: f(x,y)=x2exy&amp; the point is (x,y)=(1,1)

Q: Find a vector tangent to the curve of intersection of the two cyclinders a2 + y? = 8 and y² + 22 = 8…

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Q: A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = (4…

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Q: 2.) a.) y=fcx), X=t y = f (t) the vector egn of the plane curve is ずul-t+fc+)+o.g は13

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Q: A vector normal to the surface y-:-3 at the point (-1,-2, 2) is (a) i+2j+k (b)-i+j+2k) (e) (21 -j+k)…

A: The given surface is: xy-z=3 And, the given point is: -1, -2, 2 Since, the gradient represents a…

Q: 20. Which of the following vectors is normal to the surface In(x + y* -- z) = x-1 at the point where…

A: Given surface is

Q: 4. (8 points) Find a vector parametrization for the intersection of the plane x +y+z = 3 and the…

A: Use polar coordinates for Parameterization

Q: a) Find the point(s) on the surface S : a2 – y² + 6z = 0, where the normal line to the surface S is…

A: To find the point. Given surface is x2-y2+6z=0 Let fx,y,z=x2-y2+6z fx=2x,  fy-2y,  fz=6 The…

Q: 1. Let C be the curve of intersection of the paraboloid x2 + y? = z and the cylinder 4 - + (y – 1)²…

A: Given: The paraboloid equation is x2+y2=z and the cylinder x24+y-12=1 a) Find the vector-valued…