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Unformatted text preview: f takes on the constant value 1. 3. Consider the function f : R 2 R given by f ( x , y ) = xy 2 p x 2 + y 2 for ( x , y ) 6= In this problem, youll show lim h f ( h ) = 0. (a) For = 1/2, nd some > 0 so that when 0 < h < we have  f ( h ) < . Hint: As with the example in class, the key is to relate  x  and  y  with  h  . (b) Repeat with = 1/10. (c) Now show that lim h f ( h ) = 0. That is, given an arbitrary > 0, nd a > 0 so that that when 0 < h < we have  f ( h ) < . (d) Explain why the limit laws that you learned in class on Wednesday arent enough to compute this particular limit....
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 Fall '08
 Kim
 Calculus, Sets

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