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4 Pages

### oldexam3

Course: MATH 1220, Spring 2008
School: Southern Utah
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Word Count: 269

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3, Exam Math 1220 Fall 2005 Name Instructions: Show all of your work. (But only if you want credit!) You may not use symbolic manipulation capabilities on your calculator: Only numerical work is allowed. 1. Solve the mixing problem dQ/dt = (200 Q)/10, Q(0) = 100, using either of our two methods. (Recall for integrating factors that if = exp( p(x)) dx, then y = 1 ( (x)q(x) dt + C).) (12 pts) 2. Tell whether...

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3, Exam Math 1220 Fall 2005 Name Instructions: Show all of your work. (But only if you want credit!) You may not use symbolic manipulation capabilities on your calculator: Only numerical work is allowed. 1. Solve the mixing problem dQ/dt = (200 Q)/10, Q(0) = 100, using either of our two methods. (Recall for integrating factors that if = exp( p(x)) dx, then y = 1 ( (x)q(x) dt + C).) (12 pts) 2. Tell whether the sequence converges or diverges. If it converges, nd its limit. (6 pts each) (a) {3 (1)n } (b) {n3 e2n } 3. Tell whether the sequence is (eventually) strictly increasing, decreasing, or neither. Remember the tests: (i) Comparing an+1 an or (ii) dan /dn to 0, or comparing an+1 /an to 1. (Pts: a:8; b:6) (a) { 20n } n! (b) {an }, if d 2 (an ) = dn (2n + 3)2 4. (12 pts) Use the formula the for nth degree Taylor polynomial pn given by pn (x) = f (k) (x0 )(x x0 )k . k! k=0 n to get a 4th order polynomial approximation for f (x) = ln(x 1) about x0 = 2. 5. Find the sum of the series (if it exists). In part (b), rst nd the nth term in the sequence of partial sums to show convergence or divergence. (Pts: a:8; b:10) 5 2n+1 (a) 3n k=1 (b) k=1 ln( k+1 ) (Expand rst.) k+2 6. Test the following series for convergence or divergence. Clearly demonstrate ...

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