handout_09_16 - Math 1a Limit Laws 1 Let f be a function...

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Math 1a: Limit Laws September 16, 2009 1. Let f be a function such that f (2 . 01) = 0, f (2 . 001) = 0, f (2 . 0001) = 0, and so on. Can we conclude that lim x 2 f ( x ) = 0? 2. Suppose we know that lim x 5 f ( x ) = 3. Which of the following must be true? (a) f (5) = 3; (b) f is defined at 5; (c) if f is defined at 5 then f (5) = 3; (d) there is a number x such that f ( x ) < 3 . 05; (hint: look for x near 5) (e) there is a number x such that f ( x ) > 2 . 95; 3. Does lim x 0 1 x 2 + 1 exist? If it does, compute it. Explain your reasoning.
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