Calculus II, Fall 2014 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 04

1. Section 10.10: Problems 10, 27, 35, 37, 43, 46, 51, 64, 66.

2. Section 11.2: Problems 1, 33, 41.

3. Section 11.2: Prove the following generalization of problem 41.

Let (x(t), y(t)), a ≤ t ≤ b, be a parametrization of a plane curve and f : [0, 1] ↦ [a, b] be any monotone increasing function with continuous derivative. This gives another parametrization of the curve as (x̄(s), ȳ(s)) = (x(f(s)), y(f(s))), 0 ≤ s ≤ 1. Show that the length of (x(t), y(t)), a ≤ t ≤ b is the same as (x̄(s), ȳ(s)), 0 ≤ s ≤ 1.