WS11 - Math 152 Workshop 11 Spring 2011 1. Suppose f ( x )...

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Unformatted text preview: Math 152 Workshop 11 Spring 2011 1. Suppose f ( x ) = 2 + 3 x , and suppose that the sequence { a n } has the following recursive defini- tion: a 1 = 1; a n +1 = f ( a n ) for n > 1 . (a) Compute decimal approximations for the first 5 terms, a 1 , a 2 , a 3 , a 4 , and a 5 , of the sequence. (b) The graph to the right shows parts of the line y = x and the curve y = 2 + 3 x . Lo- cate on this graph or on a copy to be handed in the following points: ( a 1 ,a 2 ), ( a 2 ,a 2 ), ( a 2 ,a 3 ), ( a 3 ,a 3 ), ( a 3 ,a 4 ), ( a 4 ,a 4 ), ( a 4 ,a 5 ), and ( a 5 ,a 5 ). Also show a 1 , a 2 , a 3 , a 4 , and a 5 on the x-axis. (You must draw 13 points .) (c) Write a statement of a result in section 10.1 which shows that this sequence converges. You must find a specific THEOREM in the section which will guarantee convergence. (d) Compute the limit of { a n } . 2. Each of the following sequences has limit 0: 1 n n =1 1 n n =1 1 n 2 n =1 1 10 n n =1 (a) For each sequence, state exactly how large...
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WS11 - Math 152 Workshop 11 Spring 2011 1. Suppose f ( x )...

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