Find a parametrization of the circle of radius 6 in the xy-plane, centered at the origin, oriented clockwise. The point (6,0) should correspond to t=0. Use t as the parameter for all of your answers.  x(t)= y(t)=

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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Q: Find a parametrization for the cylinder x2 + y2 = 1.

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Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: Find equation of the plane tangent to the following surface at the given point. an z = tan(xy):…

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Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Find the equation of a tangent plane to the surface of z = eª cos(y) at the point P(0,0, 1).

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

Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: Find the point on the surface z = xy + 1 nearest the origin.

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Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

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Q: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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Q: Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of  [ 0,…

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Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Find a parametrization of the circle of radius 5 in the xy-plane, centered at (−4,−4), oriented…

A: If the radius of the circle is r and the centre is (h,k), oriented counterclockwise. Then the…

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: Find a parametrization of the circle of radius 8 in the xy-plane, centered at (1,−4), oriented…

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Q: y = V9a2, 0s rs1

A: Given: y=9x23, 0≤x≤1

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

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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: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find the equation of the tangent plane to the sphere x² + y? + z² = 1 at the point (1/ V3, 1/V3,…

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Q: Find an equation of the tangent plane to the given surface at specified point. a) z = e*y +…

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Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: Consider the plane curve C ∶ r(t)=(1/3t^3, 1/2t^2) (a)Make a table of values and sketch the curve…

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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 a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

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: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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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 a parametrization for the curve that matches the lower side of the parabola x-1=y2. A. x =…

A: Solution:

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: Use numerical integration with Ax = 1.0 m to locate the centroid of the surface generated by…

A: Given That : y=3x216 and ∆x=1.0 m To find : locate the centroid of the surface generated by…

Q: Find an equation for the plane tangent to the surface e'z = x cos(xz) – y at the point (2, 1, 0).

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Q: Find the work done by the force field F(x,y)=5x2i−2xyj on a particle that moves once around the…

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Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

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

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: Find a parametrization of the circle of radius 4 in the xy-plane, centered at the origin, oriented…

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Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

A: Given F→(x,y) = -ysin(x)i→+cos(x)j→ a) Let us assume x=t then y=x2=t2 by differentiating r→(t) with…

Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters:

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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