Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi] to find the area that encloses it.

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: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Consider the surface S parametrized by R(u, v) (uv, sin u, cos v). Find an equation for the tangent…

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Q: Which of the following is the surface area of the solid body created by rotating the given…

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

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Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

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Q: Find the area of the surface obtained by rotating the curve x = 6 cos 0, y = 6 sin³ 0, 0< 0 <n/2 %3D…

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Compute the surface area of the surface generated by revolving the astroid with parametrization c(t)…

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Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s &amp; t as two parameters radius = a and height…

Q: Find parametric equations for the surface generated by revolving the curve y = 1/x about the x-axis.

A: When y = f(x) is rotated about x axis, we get a surface with parametric representation is,…

Q: Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0 < 2m, to find the area…

A: Given Parametric Equation of ellipse  x=acosθ and y=bsinθ ,0≤θ≤2π To find the area of the Ellipse

Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x², 0sis…

A: y=1-x2,  0≤x≤12 Differentiating with respect to x, we get dydx=121-x2·0-2x=-x1-x2

Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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Q: Find the surface area of the solid that is obtained by rotating the graph of the parametric curve…

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Q: Consider the parametric equations below. x = t sin(t), y = t cos(t), 0sts" 3 Set up an integral that…

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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 the length of arc of the curve given by the parametric equations x = t°, y=t² from the point…

A: Arc length is given byL=∫abdxdt2+dydt2dt

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Find the area of the surface of revolution generated by revolving the curve r = 2acos(theta) about…

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find the area of the surface generated by revolving the curve

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the…

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

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: Use the parametric equations of an ellipse x = 10 cos 0 y = 22 sin 0 0 ≤ 0≤2T to find the area that…

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Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

Q: Find an equation of the tangent(s) to the curve with parametric equations tsint at the point…

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2T, to find the area…

A: Given: Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π,  to find…

Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

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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: Give a parametric description for a sphere with radius a, includingthe intervals for the parameters.

A: We will use the spherical coordinates for parametrization. Where ρ= radius= a And,

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

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

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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: The area of the rotational surface resulting from rotating x² + y2 = a² about the x axis is? the arc…

A: Given : x2 + y2 = a2

Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: Find an equation of the tangent plane to the parametric surface x=5rcosθ, y=4rsinθ z=r at the point…

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Q: Evaluate integral and use parameter t to show parametric equations for circle ∫c x6y d s where C…

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Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: Consider the parametric equations below. x = In(t), y = Vt+ 1, 4sts6 Set up an integral that…

A: Explanation of the answer is as follows

Q: Find the area of the surface obtained by rotating the curve of parametric equations: 6 x = 6t – t, y…

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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: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…