3. Consider the curve y = x°, 0

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: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: Find the general equation of the circle of curvature of the parametric equation t+1 X: ; y = ±…

A: This is a problem of finding equation of the circle of curvature. Based on the general formula and…

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: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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

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

A: Given surfaces are And the given point P is

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: Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t)…

A: Introduction :

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

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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: 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: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating…

A: Sketch the plane curve represented by the parametric equations             x=t     and     y=2t-1 by…

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

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: Sketch the surface represented by the parametric equations x = cos³ t and y=sin³ t with 0st≤n/2.…

A: Given: x=cos3t and, y=sin3t we have to find the surface area by rotating about x-axix. Suppose the…

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: z = In(x²y*) + / x² + y²

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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 following: (a) the general equation of the tangent plane to the surface at Po (b) the…

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Q: 3- Determine the area of the region below the parametric curve given by the following set of…

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

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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: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…

A: Recall: sin2t+cos2t=1

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

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

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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

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

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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: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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

A: Solution-

Q: let C be the curve of intersection of the 3-D graph of x2=2y (a "parobolic cylinder") with the graph…

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

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 an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the…

A: Our Aim is to find an equation for the surface of revolution formed by revolving the curve 2x+3z=1…

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

A: Topic = Functions

Q: Find the area of the surface obtained by rotating the curve of the following parametric equations…

A: We need to find surface area.

Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

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: 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: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

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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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