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c1-t2-a - NAME: Em Toidi [Briefs] TEST2/MAC2311 Page 1 of 4...

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NAME: Em Toidi [Briefs] TEST2/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. Communicate. Show me all the magic on the page. Eschew obfuscation. ______________________________________________________________________ 1. (25 pts.) Compute the first derivatives of the following functions. You may use any of the rules of differentiation that are at your disposal. Do not attempt to simplify the algebra in your answers. You should do minor arithmetic, however, to have clean constants. (a) (b) (c) (d) (e) ______________________________________________________________________ 10 point Bonus: Provide a rigorous ε - δ proof of the limit Let ε > 0 be arbitrary. Set . We’ll now show this δ does the job. Suppose x is a real number such that 0 < x < δ . Then The key to the magic above is the inequality which you can see in a slightly different form in Problem 8. Another natural δ to use is δ = min( 1, ε /2 ), where x 2 x .
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TEST2/MAC2311 Page 2 of 4 ______________________________________________________________________ 2. (10 pts.) (a) Using complete sentences and appropriate notation, provide the precise mathematical definition of continuity of a function f(x) at a pointx=a .
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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-t2-a - NAME: Em Toidi [Briefs] TEST2/MAC2311 Page 1 of 4...

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