R(u, v) = (3 sin(2u), 6 sin² u, v) (0 ≤u≤T

Q: Plot the set of parametric equations by making a table. You mušt indicate the orientation…

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Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: 3. Set up the triple integral now for two problems you already worked on: (a) The volume of the…

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Q: Find the Cartesian equation of a curve defined parametrically by 5t and y =10t for all real values…

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Q: =urface at the given point. y? at the point (3, 2, 2) 9.

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Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

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Q: Investigate the direction of convexity of the curve defined by the parametric…

A: To Determine: The direction of convexity of parametric curves x(t)=a(t-sint) , y(t)=a(1-cost) ,…

Q: Find the equation of the tangent plane to z = e + x + x* + 10 at the point (4, 0, 79). Submit answer

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Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the tangent plane to the equation z = 7e²²-2y at the point (4, 8, 7) 2 II

A: Given:The equation is  and the points are .To Find:The equation of the tangent plane through  is…

Q: C- Find unit vectors tangent and normal to the curves (y=4sine x-1-3cos8) at 8=:

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Q: Find a parametric description for the unit circle, beginning at (0,1) at time t=0 , and completing…

A: Parametric equation

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: 22. Eliminate the parameter from the parametric equations x= -√fy-4t+20sts4

A: To eliminate the parameter to get the Cartesian equation

Q: Consider the parametric function given below by the equations x=-t +2 y = t² – 2 for t in the…

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Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

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Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

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

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: No.24.31. differential equations

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Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…