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# Convergence or Divergence, Taylor Polynomials, Maclaurin Series and Chain Rule

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1. Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so {see attachment}

2. Find the open interval of convergence and test the endpoints for absolute and conditional convergence: {see attachment}

3. For the equation f (x) = ... {see attachment}
- find the Taylor polynomial of degree 4 of at c=4.
- determine the accuracy of the polynomial at x=2

4. Find the Maclaurin series in closed form of: {see attachment{

5. Use the chain rule to find dw / dt, where: {see attachment}

6. Find the critical points and test for relative extrema: {see attachment}

7. Maximize {see attachment} given the constraint x+y-2 = 0

Please see the attached file for the fully formatted problems.

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#### Solution Summary

Convergence or Divergence, Taylor Polynomials, Maclaurin Series and Chain Rule are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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