Syllabus and Homework: Part I

(additional non-book problems below are also required)

Feb 7-11: §7.4, §11.3, §11.4 (omit integral test) in Anton

Feb 14-18: §11.6, §11.7 in Anton

§11.6: 12, 14, 16, 18, 26, 30, 44, 46
§11.7: 5, 8, 10, 22, 28, 48
A: Find all x such that the following series converges:

$\begin{displaymath}\sum_{n=1}^{\infty} n\left( {x\over 5x+6}\right)^n\end{displaymath}$

Feb 21-25: §11.8, §11.5 in Anton

§11.8: 5, 6, 8, 10, 14, 18, 30
§11.5: 1, 7, 10, 12, 16, 22, 24
A: If $\sum a_n x^n$ has radius of convergence 5, what is the radius of convergence of $\sum a_n x^{2n}$ ?

Feb 28-March 3: §11.10, §11.9 (begin) in Anton

§11.10: 6, 16, 26, 33(a)(b), 34(a)(b)
A: Find the unique power series $f = \sum b_n x^n$ so that $f'(x) = \sin(x)/x$ if $x \ne 0$ and f(0) = 1. What is its radius of convergence?
§11.9: 3, 4, 6 (ignore ``calculating utility'' business in these problems)
B: Find the Maclaurin series for $\ln ((1+2x)(1+5x))$ .

March 6-10: §11.9 (finish) in Anton, review

§11.9: 16 (ignore ``calculating utility'' business in this problem), 18(a), 20(a), 22
A: Find the Maclaurin series for ${1\over \sqrt{1+x}}$ .
B: Use the identity $\int {1\over \sqrt{1-x^2}}\, dx = \sin^{-1}x +C$ to find the first four nonzero terms in the Maclaurin series for $\sin^{-1}x$ .

Exam on Tuesday, March 14, 6:30-8:30pm, Science Center C

Thomas J. Brennan
2000-01-31