10. Sketch the following surfaces (graphs of functions) for a = 2, b = 1: (a) Elliptic paraboloid. M: z = +. Show that Nи, v) - (аи сos v, bu sin v, ue'), и>0, is a parametrization that omits only one point of M. x y? (b) Hyperbolie paraboloid. M: z = - a? b Show that M is covered by the single patch x(u, v) = (a(u + v), b(u – v), 4uv) on R².

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4.2-10 only part b

10. Sketch the following surfaces (graphs of functions) for a = 2, b = 1:
(a) Elliptic paraboloid. M: z = +. Show that
Nи, v) - (аи сos v, bu sin v, ue'), и>0,
is a parametrization that omits only one point of M.
x y?
(b) Hyperbolie paraboloid. M: z = -
a? b
Show that M is covered by the single patch
x(u, v) = (a(u + v), b(u – v), 4uv) on R².
Transcribed Image Text:10. Sketch the following surfaces (graphs of functions) for a = 2, b = 1: (a) Elliptic paraboloid. M: z = +. Show that Nи, v) - (аи сos v, bu sin v, ue'), и>0, is a parametrization that omits only one point of M. x y? (b) Hyperbolie paraboloid. M: z = - a? b Show that M is covered by the single patch x(u, v) = (a(u + v), b(u – v), 4uv) on R².
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