Calculus I, Fall 2015 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 07

1. Section 3.11: problems 9, 11, 17, 63, 64.

2. The error formula for linear approximation L(x, x_{0}) (also denoted as L(x) sometimes) is not mentioned explicitly in the textbook till a later Chapter. Just take it for granted and memorize it for now:

f(x) − L(x, x_{0}) = \frac{1}{2}f′′(c)(x − x_{0})^{2}

where c lies between x and x_{0}. As a consequence, we have an error bound

|f(x) − L(x, x_{0})| ≤ \frac{1}{2} ( max_{c between x and x_{0}} |f′′(c)|) (x − x_{0})^{2}

Use this formula to give an estimate on the error of linear approximation for problem 17 (b) of Section 3.11.

3. Chapter 3, additional and advanced problems: problems 21, 23.

4. Section 4.1: problems 27, 35, 39, 59, 77, 93.