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c1-t1 - NAME TEST1/MAC2311 Page 1 of 4 Read Me First Show...

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NAME: 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 (b) lim z 1 1 1 z (c) lim x 1 x 3 x 2 x 101 (d) lim x → ∞ 2 ln( x ) (e) lim h → ∞ 6 1 h _________________________________________________________________ 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 ) (b) lim x h( x ) (c) lim x 1 h( x ) (d) lim x 2 h( x ) (e) lim x 3 h( x )
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TEST1/MAC2311 Page 2 of 4 _________________________________________________________________ 3. (25 pts.) For each of the following, find the limit if the limit exists. If the limit fails to exist, say so. Be as precise as possible here. [Work on the back of Page 2 of 4 if you run out of room here.] (a) lim x 3 x 2 2 x x 1 (b) lim x 1 x 4 1 x 1 (c) (d) lim x 1 4 x 4 x 1 (e)
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