Calculus II, Spring 2019 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 05

1. Section 10.9: Problems 7, 9, 17, 19, 33, 41, 42, 50(a), 51. Hint for problem 50(a): use the fact sin P = sin(π − P). Remark: (Optional, not part of homework assignment) If you are interested, you can observe how fast this iteration P_{k} ↦ P_{k+1} = P_{k} + sin(P_{k}) converges to π. Try, for example, the following commands in matlab: format long; P = 2; P = P + sin(P); error = abs(P-pi) Repeat the last command a few times (using the ’upper arrow’ key in your keyboard), you will see the error decreases rapidly. It converges even faster than Newton’s method.

2. Section 10.10: Problems 10, 19, 27, 64, 65.

Remark: The following are homework assignments for week 6: Section 10.10: Problems 31, 35, 37, 43, 46, 66, 74.