quiz1-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

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Unformatted text preview: AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Quiz # 1: Prerequisites Test Solution Notes 1. Find all numbers x satisfying 2- 1 /x = 1 / (1 + x ). 2- 1 x = 1 1 + x 2 x- 1 x = 1 1 + x (2 x- 1)(1 + x ) = x 2 x + 2 x 2- 1- x = x 2 x 2 = 1 x {- radicalbig 1 / 2 , radicalbig 1 / 2 } 2. g ( t ) is an exponential function, and g (0) = 10, and g (3) = 80. Find an expression for g ( t ). Since g ( t ) is exponential, we know that g ( t ) = Ab t , for some A , b . We know that g (0) = 10; thus, A = 10. We know g (3) = 80, so 10 b 3 = 80, so b 3 = 8, so b = 2. Thus, g ( t ) = 10 2 t . 3. Solve this equation for t : y = b + a ( t 1) t +1 . yt + y = bt + b + at- a y + a- b = ( b + a- y ) t t = y + a- b a + b- y 4. The inequality 2 | 2- x | > 2 3 describes a subset of the real line (the subset of numbers x for which the inequality holds). Describe this subset. We know that | 2- x | > (1 / 3). Thus, 2- x > (1 / 3) OR 2- x <- (1 / 3). Thus, x < 5 / 3 OR x > 7 / 3. This can be written also as...
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This note was uploaded on 02/07/2010 for the course AMS 151 taught by Professor Zhang during the Fall '08 term at SUNY Stony Brook.

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quiz1-sol - AMS 151 (Fall, 2009) Joe Mitchell Applied...

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