Unformatted text preview: ( u, v ) = ( uv, u 2 + v 2 ) at ( a, b ) = (3 , 10). 2. Let R = [0 , 1] × [0 , 1] ⊂ R 2 . i) Suppose we have a ²nite subset of R : E 1 = { ( x k , y k ) : 0 ≤ x k , y k ≤ 1 , k = 1 , . . ., N } . Show that for any ǫ > 0 there exists a grid G 1 such that V ( E 1 ; G 1 ) < ǫ . ii) For E 2 = { ( x, y ) ∈ R : x = y } show that for any ǫ > 0 there exists a grid G 2 such that V ( E 2 ; G 2 ) < ǫ . iii) For E 3 = { ( x, y ) ∈ R : x 2 + y 2 = 1 } show that for any ǫ > 0 there exists a grid G 3 such that V ( E 3 ; G 3 ) < ǫ . Remark. I made a correction on 1c). 1...
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 Winter '07
 Fukuda
 Empty set, MAT 125B Homework, grid G1

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