MAC 2312 Midterm: MAC2312 S99 Test 3
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March 29, 1999: (10 pts. ) lim, (10 pts. ) lim x 1 ln x20 x2 1 x 1 + 1 x : (10 pts. ) lim x x2 x + 1, (10 pts. ) n 1 lim. 1 x2 dx : (15 pts. ) Find p3(x), the taylor polynomial of order 3 for f (x) based at a = 1. Find a formula for r3(x), the remainder for. Obtain a good bound for |r3(0. 5)|: (10 pts. ) If an = ( 1)n n! write the rst ve terms of the sequence, starting with a1. If it converges, nd the limit lim an = n : (10 pts. ) Find an explicit formula for the nth term an of the sequence:
