c1-t3-a

c1-t3-a - NAME Em Toidi[Briefs TEST3/MAC2311 Page 1 of 5...

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NAME: Em Toidi [Briefs] TEST3/MAC2311 Page 1 of 5 ______________________________________________________________________ Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Do not "box" your answers. Communicate. Show me all the magic on the page. Eschew obfuscation. ______________________________________________________________________ 1. (10 pts.) Write down each of the following derivatives. [2 pts/part.] (a) (b) (c) (d) (e) ______________________________________________________________________ 2. (10 pts.) (a) Use logarithmic differentiation to find dy / dx when Thus, (b) Find dy / dx when We must use implicit differentiation here. First, pretend that y is a function of x . Then
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TEST3/MAC2311 Page 2 of 5 ______________________________________________________________________ 3. (10 pts.) (a) (6 pts.) Find formulas for y and the differential dy when y = x 2 . Label your expressions correctly. Evidentally dy = (2 x ) dx is cheap thrills, but y is only slightly messier. (b) (4 pts.) Use an appropriate local linear approximation formula to estimate . Let f ( x ) = x 1/2 and set x 0 = 25. Then the local linear approximation at x 0 is given by for all x . When x = 24.9, . ______________________________________________________________________ 4. (10 pts.) (a) Let . Show that f is one-to-one on (0, ) using f . [A little explanation is needed!] Since f
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c1-t3-a - NAME Em Toidi[Briefs TEST3/MAC2311 Page 1 of 5...

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