09.19 - [Collect summaries of section 1.4] [Hand out...

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Unformatted text preview: [Collect summaries of section 1.4] [Hand out time-sheets for assignment #3] Section 1.3: The notion of limit (continued) Claim (see Example 1 from p. 24): If A ( h ) = 4.9(10+ h ) for all h 0, lim h A ( h ) = 49. Bad proof: Just plug in h = 0. Whats wrong with it is that, in general, lim x a f ( x ) need not equal f ( a ). Later on, well prove general theorems that guarantee that in certain fairly broad situations, lim x a f ( x ) = f ( a ). When we can appeal to one of those theorems, we get to say Since f ( x ) is continuous at a , we can just plug in x = a and thatll count as a valid proof. But were not there yet; so for now we have get down and dirty with epsilons and deltas. To show that lim h A ( h ) = 49 is TRUE, we need to show that for every > 0 there is a number > 0 such that if 0 < | h | < , | A ( h ) 49| < . To figure out what we need (which will depend on ), lets rewrite | A ( h ) 49|: since A ( h ) = 4.9(10+ h ), we have | A ( h ) 49| = |4.9(10+) 49| = |4....
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This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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09.19 - [Collect summaries of section 1.4] [Hand out...

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