Thomas’ Calculus Early Transcendentals 12ed

Homework Assignment for Chapter 11

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

2. 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.

3. Section 11.4: Problems 14, 19, 21.

4. Section 11.5: Problems 7, 20, 23.