3. Consider the curve y = x³, 0 < x < 3. (a) Find parametric equations for the surface obtained by rotating this curve about the x-axis. (b) Compute the area of this surface.

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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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: EXAMPLE 9 Find the tangent plane to the surface with parametric equations x = u2, y = v2, z = u + 2v…

A: Given parametric equation x=u2 , y=v2 , z=u+2v

Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: 3) Find the radius of curvature for the parametric curve e-t cost , y = e-t sin t.

A: Given parametric curve is x=e-tcost, y=e-tsint. We know that the Radius of curvature of a parametric…

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x2 , (z =…

A: The distance of any points ( having same y co-ordinate ) on the curve is at same distance from…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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Q: find the areas of surfaces generated by revolving the curves about the given axes

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

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Q: Find an equation for the tangent plane and find the parametric equations for the normal line to the…

A: I am attaching image so that you understand each and every step.

Q: Find the equation of the surface of revolution generated by revolving the curve z²=4y in the…

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Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: 3) Find the radius of curvature for the parametric curve e-t cost, y = e-t sin t.

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Q: The parametric curve X= 2sin(t) + 2, y=3cos(t) – 2 describes a clockwise traveling vertical ellipse…

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

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

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: Given the surface z = In(5x2 + 2xy - 3y2 – 12). (a) Find the equation of the tangent plane and the…

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Q: x =9+2t² y = 4t 0St<2 about x-axis

A: SURFACE AREA OF PARAMETRIC CURVE:                    Consider the parametric curve given by…

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x.(z 0)

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Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

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Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0

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Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: 1-) Given the surface z = In(-2x2 + 5y2 – xy). Find the equation of the tangent plane and the…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: 3) Find the radius of curvature for the parametric curve x = e-t cost , y = e-t sin t.

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces tan-1(x?…

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Q: Find the equation of the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

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Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A: Given surfaces, x2+2y+2z=4     and   y=1f(x,y,z)=x2+2y+2z-4          and   f(x,y,z)=y-1  And point…

Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…

A: x=5cost,  y=2sint Now,…

Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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Q: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

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