Q7. Consider a large circle of radius R > 0 centered at the origin. Suppose that a small circle of radius r< R is centered at (0,R + r). Let c(0) be a marked point (0,R + 2r). Allow the small circle to travel with angular velocity d0/dt =1 around the outside of the large circle while remaining tangent to it. Parametrize the curve c(t) traced by the marked point

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

A: Explained below

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

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…

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A: x=5t-9y=12t-3

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

A:

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

A:

Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

A:

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

A:

Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: 4. The position of a particle at time t is given by x(t) = 5+4 sin(t) y(t) = 2 − 4 cos(t) 0<t</ (a)…

A: This is a problem of parametric curve and Integration.

Q: The curvature of a point moving along the curve given as R(t)=(ln sec t) i+ tj is

A:

Q: Find the equation of the tangent plane to the given surface at the point P. x2 + y2 + z2 = 9, P =…

A: Concept Used:- For an implicitly defined function f(x, y, z)=0 The equation of the tangent plane to…

Q: Let y = f(x) be defined parametrically as y = f + as y=t+tt, x = 2t -tl, te R. Find f(x) and discuss…

A:

Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

A: