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

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.