Unformatted text preview: (a) f ( x ) = sin1 ± 2 x ¶ (b) For f ( x ) = sinh(2 x ), ﬁnd 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, ﬁnd 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 diﬀerentiation” (show your work) to ﬁnd 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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This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.
 Winter '98
 MathDep
 Slope

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