Unformatted text preview: D ( f1 ) f ( x ) . (b) Give an example of a diFerentiable, invertible function whose inverse is not diFerentiable. 3. Consider the set S ⊂ R 5 de±ned by the equations x + 2 y + z = u + v xyz = uv 1 π sin ( ( x + 2 y + 3 z ) π ) + 1 = exp(5 u3 v ) . Show in a neighbourhood of the point a = ( u, v, x, y, z ) = (6 , 10 , 3 , 4 , 5) that x, y, and z can be given as C 1 functions of u and v . Also, ±nd vectors w 1 , w 2 ∈ R 5 such that { a + sw 1 + tw 2 : s, t ∈ R } is the tangent plane to S at the point a . No late assignments. 1...
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 Fall '09
 RomauldStanczak
 Calculus, Multivariable Calculus, Continuous function, Inverse function, Multiplicative inverse, Inverse element

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