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Unformatted text preview: . EXERCISES: You do not need to submit these questions but you should make sure that you are able to answer them; 1. Spivak # 5.8, 5.9, 5.10(a), 5.12, 5.13, 5.16, 5.18, 5.33(i)(iii), 5.38(b), 5.39(v)(vi). 2. Give a precise denition for each of the following limits: (a) lim x a f ( x ) = , where a R . (b) lim x a + f ( x ) = , where a R . (c) lim x f ( x ) = . (d) lim x  f ( x ) = , where R . 3. Let a, L R . Suppose that lim x a f ( x ) = L. Provide a complete and accurate  proof that lim x a ( f ( x )) 2 = L 2 . 4. Show that: lim x 3 1 ( x3) 2 = . (This is Spivak # 5.37(a)). 2...
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 Summer '11
 Katherine
 Math

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