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Please do like
- Find the area of the surface with parametric equation X=2², yuv, 2 = va and...
differential geometry
2. Find the parametric equation of a circular helix with x-2t-|.
2. Find the parametric equation of a circular helix with x-2t-|.
7. Find an equation of the tangent plane to the given parametric surface r(u, v) = uvi+u sin(n)j + v cos(u)k, at u = 0, v = . 8. Find the area of the part of the surface 2 = 2 + 5x + 2y that lies above the triangle with vertices (0.0), (0,1), and (2,1).
find surface area and volume using carestian equation and not
parametric
(use disc method for the volume)
An asteroid is particular mathematical curve: a hypocycloid with four cusps. It is formed by rolling a circle (shown in black) inside a fixed circle (shown in blue) with four time the radius. The trajectory of an asteroid is shown in Figure 1. Figure 1: Trajectory of an asteroid If the radius of the fixed circle is a, then the equation of an...
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1.
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
find an equation of the tangent plane and parametric equations
of the normal line to the surface at the given point
z=-9+4x-6y-x^2-y^2 (2,-3,4)
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
Find an equation of the tangent plane to the given parametric surface at the specified point.r(u, v) = u cos vi + u sin vj + vk; u = 9, v = p/3
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
5. Suppose σ is a parametric surface with vector equation r(14. u) x (u, u)i + y(u, u)j + z(u, v)k If σ has no self-intersections and σ 1s smooth on a region R in the uu-plane, then the surface area of ơ is given by
5. Suppose σ is a parametric surface with vector equation r(14. u) x (u, u)i + y(u, u)j + z(u, v)k If σ has no self-intersections and σ 1s smooth on a region R...
osts 1 = e' sint y=e' cost parametric equation of the curve part; a) find the length, b) Find the area of the surface formed by rotating it around the Ox- axis.