MATH 4B – STUDY GUIDE, CHAPTER 10

1. Does the sequence converge or diverge? If it converges, find the limit.

2. What kind of series is ? Does it converge or diverge? Why? Find the sum, if it is possible and reasonable to do so without a calculator. Use interals to find the minimum and maximum possible errors in using S₁₀₀ to estimate S

3. What kind of series is? Does it converge or diverge? Why? Find the sum, if it is possible and reasonable to do so without a calculator.

4. Apply the divergence test (kth term test) to the series . Based only on this test, can you prove that the series converges or diverges or must you apply a different test? If the divergence test cannot be used, apply an appropriate test to check convergence.

5. Apply the appropriate test to determine whether converges absolutely, converges conditionally or diverges. Find the greatest possible error that could result from using the first 500 terms to estimate the overall sum.

6. Find the radius and interval of convergence of the series Make sure you test for convergence or divergence at the endpoints of the interval of convergence.

7. Find the first 5 terms of the Taylor polynomial and the Taylor remainder for the function f(x)=sin x expanded about (that is, x₀=).

8. Use the Maclaurin series for f(x)=e^x to derive a series for and use the first four terms to approximate (Simplify algebraically, but leave your answer is a form that permits you to predict additional terms by examination. Do not spend time calculating a single numerical answer).

Return to: Merced College; Don Power Updated 11/24/04 by Don Power