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Unformatted text preview: (a) f ( x ) = sin1 2 x (b) For f ( x ) = sinh(2 x ), nd f (0). Give a numerical value. 7. [10] Carbon14 decays exponentially and its halflife is about 5700 years. (a) For an initial 5 lb. amount of Carbon14, nd the function, y ( t ), that describes how much is left after t years. (b) Suppose that charcoal from a tree that was killed during the volcanic eruption when Crater Lake was formed now contains 2/5 (40%) of its original Carbon14. How long ago did the eruption occur? 8. [8] Find the minimum values of the function f ( x ) = x ln x . 9. [8] Use logarithmic dierentiation (show your work) to nd the derivative of y = (1 + x ) 2 x . 10. [10] Calculate each integral: (a) Z 1 x (ln x ) 2 dx (b) Z 1 1 + 9 x 2 dx 11. [6] Calculate the limit. Show each step: lim x x 2 ex...
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 Winter '98
 MathDep
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