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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 deﬁnition 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 δ± 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, Calculus, Logic, Englishlanguage films, Following, lim

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