Please calculate the surface area of revolution obtained by rotating the following parametric curve with respect to a axis. [x = t² /2 0st<1.

Q: Determine the area of the surface obtained by rotating the curve. y=[(x4)/16] + [1/(2x2)] ;…

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Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: B- Find the area of the surface generated by revolving the curve y = √2-x² about x-axis

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Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = &lt;t, t2&gt;That implies,

Q: Find an equation of the tangent plane to the given surface at the specified point. ²², (1, -1, 1)

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Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y? + 6, (1, 3, 16)

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