quiz1-sol

# quiz1-sol - AMS 151(Fall 2009 Joe Mitchell Applied Calculus...

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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 x ( -∞ , 5 / 3) (7 / 3 , ), a union of two halflines. 5. Find the equation of the line through point (2,3) that is perpendicular to the line 2 y + x = 5.

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