17AMI.F09 - lim a n n" Justify your answer 6 Use log...

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17A Midterm I (Benham) Fall 2009 1. a) Find the domain and range of f ( x ) = 4 x 2 ! x ( ) x + 3 ( ) b) Solve 3 x ! 5 " 4 2. A population triples every time step. a) Find its exponential model, given that the initial population is n 0 = 4 b) Find the recursion relation describing this model. 3. Determine the first four terms of the sequence defined by a n = n ! 1 ( ) n + 1 ( ) n 2 + 2 b) Find lim n !" a n : Justify your answer. 4. Use the Intermediate Value Theorem to determine whether the equation e ! x = x has a solution on the interval (0, 1). 5. The recursion relation a n + 1 = 3 a n 1 ! a n ( ) with a 0 = 1/ 3 defines a unique sequence. a) Find all fixed points for this recursion. b) Find
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Unformatted text preview: lim a n : n !" Justify your answer. 6. Use log transforms to change each of the following functions to a linear relationship. in each case determine whether a og – log or a log – linear plot should be used to graph that linear relationship. a) y = 3 e ! 2 t b) z = 2 x 3.5 7. Find the following limits. In each case, justify your answer. a) lim x !" 2 1 5 x 2 " 4 b) lim x ! sin 2 x x c) lim x ! 3 + x " 1 x 2 " 9 8. For each of the following functions, determine all values of f(x) where f(x) is continuous. a) f(x) == tanx b) f(x) = x 2 + x ! 6 x ! 2 c) f x ( ) = ln x ( ) x 2 + 1...
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This note was uploaded on 05/31/2011 for the course MATH 17A taught by Professor Lyles during the Spring '08 term at UC Davis.

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