Calculus I, Fall 2012 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 03

1. Section 3.1: problems 40, 49.

2. Section 3.2: problems 17, 21, 25, 27, 33, 37(Remark: read Example 13 in section 3.2), 57, 67.

3. Read section 3.3 on definition for average rate of change (velocity) and instant rate of change (velocity).

4. Section 3.4: problems 15, 19, 27, 53.

5. Section 3.5: problems 13, 21, 23, 29, 39.

6. (s3.5 extra1)

\frac{d}{dx}(f_{1}(x)f_{2}(x) ⋯ f_{n}(x)) =?

\frac{d^{n}}{dx^{n}} (f(x)g(x)) =?

7. (s3.5 extra2)

Show (and memorize) that

\begin{aligned}\frac{d}{dx} | \begin{matrix}f(x) & g(x) \\ h(x) & k(x) \end{matrix} | & = | \begin{matrix}f′(x) & g(x) \\ h′(x) & k(x) \end{matrix} | + | \begin{matrix}f(x) & g′(x) \\ h(x) & k′(x) \end{matrix} | \\ & = | \begin{matrix}f′(x) & g′(x) \\ h(x) & k(x) \end{matrix} | + | \begin{matrix}f(x) & g(x) \\ h′(x) & k′(x) \end{matrix} | \end{aligned}

using product rule. What is the corresponding formula for a 3 by 3 determinant? How about 4 by 4, etc?