c1-t3(1) - NAME TEST3/MAC2311 Page 1 of 5 Read Me First...

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NAME: 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.) (a) (6 pts.) Find formulas for y and the differential dy when y = x 2 - 2 x + 1. Label your expressions correctly. (b) (4 pts.) Use an appropriate local linear approximation formula to estimate (3.02) 4 . ______________________________________________________________________ 2. (10 pts.) (a) Use logarithmic differentiation to find dy / dx when y ( x 3 2 x ) ln( x ) (b) Find dy / dx by using implicit differentiation when cos( xy ) y .
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TEST3/MAC2311 Page 2 of 5 ______________________________________________________________________ 3. (10 pts.) (a) Let f ( x ) e x 3 x Show that f is one-to-one on using f . [A little explanation is needed!] (b) Suppose that a one-to-one function f has a tangent line given by y = 5 x + 3 at the point (1,8). Find f -1 (8) and ( f -1 ) (8).
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