Calculus II, Spring 2016 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 04

1. Section 10.7: odd problems in problem 41-55.

2. Find the first few terms of the power series representation of

\frac{1 − x^{2} + x^{4} − ⋯}{1 − \frac{x^{2}}{2!} + \frac{x^{4}}{4!} − ⋯}

3. Section 10.8: Problems 7, 9, 11, 15, 29, 33, 35, 41.

4. Let

f(x) = \{ \begin{matrix}0, & x = 0 \\ e^{−1/x^{2}}, & x ≠ 0 \end{matrix}

It is known that f^{(n)}(0) = 0 for all n. Verify this for f′(0) and f′′(0).