test2math1501 - 42 million radioactive atoms in that cite....

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Georgia Tech FALL 2009 Heinrich Matzinger QUIZ 2 FOR MATH 1501: CALCULUS I 1) Explain why for f ( x ) = x 2 , we have f 0 ( x ) = 2 x . 2) Show that ( f ( x ) · g ( x )) 0 = f 0 ( x ) · g ( x ) + f ( x ) · g 0 ( x ) . 3) Let f ( x ) = x 2 + 3 x . What is f 0 ( x ) equal to? 4) Calculate f 0 ( x ) where f ( x ) = sin( x ) x 3 . We assume that x is not equal to 0. 5) Let f ( x ) = 1 x . What is f 0 ( x ) equal to? Again we assume x di±erent from 0. 6) Let f ( x ) = x + 1. What is f 0 ( x ) equal to? We assume x is strictly larger than - 1. 7) Let f ( x ) = x 0 . 1 . What is f 0 ( x ) equal to? 8) Assume that f ( t ) denotes the number of radioactive atoms in a contaminated cite at time t expressed in million. Assume that now is t = 0 and that at the present moment there are
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Unformatted text preview: 42 million radioactive atoms in that cite. Hence f (0) = 42. Assume that the curve f ( t ) is nice and smooth and that f (0) =-2. The time unit is the year. What is in 36 days after t = 0 approximately the number of atoms going to be equal to in that cite? Why? 9) Let f ( x ) be equal to f ( x ) = cos( x ) x . Calculate f ( x ). 10) Calculate the limit lim x sin(2 x 3 + 3 x 2 ) x 3 + x...
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This note was uploaded on 11/12/2009 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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