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# c1-t1-a - NAME: Em Toidi [Briefs] TEST1/MAC2311 Page 1 of 4...

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NAME: Em Toidi [Briefs] TEST1/MAC2311 Page 1 of 4 _________________________________________________________________ Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Since the answer really consists of all the magic transformations, do not "box" your final results. Communicate. Show me all the magic on the page. _________________________________________________________________ 1. (10 pts.) Here are five trivial limits to evaluate: (a) lim x 0 x x lim x 0 x x 1 (b) lim z 1 1 1 z lim z 1 1 z 1 (c) lim x 1 x 3 x 2 x 101 ( 1) 3 ( 1) 2 ( 1) 101 ( 1) 101 1 (d) lim x →∞ 2 ln( x ) 0 (e) lim h 6 1 h 6 0 6 _________________________________________________________________ 2. (15 pts.) Suppose that h( x ) 2 x x 3 , if x <2 1, if x 2 x 2 8 3 x 3 , if x >2 Evaluate each of the following easy limits. (a) lim x h( x ) lim x x 2 8 3 x 3 0 (b) lim x h( x ) lim x (2 x 3 ) (c) lim x 1 h( x ) lim x 1 (2 x x 3 ) 1 (d) since lim x 2 h( x ) does not exist and lim x 2 h( x ) lim x 2 (2 x x 3 ) 4 lim x 2 h( x ) lim x 2 x 2 8 3 x 3 4 24 .

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## This note was uploaded on 12/26/2011 for the course MAC 2311 taught by Professor Staff during the Fall '08 term at FIU.

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c1-t1-a - NAME: Em Toidi [Briefs] TEST1/MAC2311 Page 1 of 4...

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