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### problems2

Course: MATH 125, Fall 2008
School: UC Davis
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Word Count: 480

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Problems Practice Easy problems: 1. The unit sphere in R3 is the set S 2 of all points (x, y, z) such that x2 + y 2 + z 2 = 1. For what points (x0 , y0 , z0 ) is it possible to nd a C 1 function z(x, y) dened near (x0 , y0 ) such that z(x0 , y0 ) = z0 and x2 + y 2 + z(x, y)2 = 1? 2. Let f (x, y) = (ex cos(y), ex sin(y)). Show that f is locally invertible everywhere, but not invertible. 3. Find the equation of the...

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Problems Practice Easy problems: 1. The unit sphere in R3 is the set S 2 of all points (x, y, z) such that x2 + y 2 + z 2 = 1. For what points (x0 , y0 , z0 ) is it possible to nd a C 1 function z(x, y) dened near (x0 , y0 ) such that z(x0 , y...
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