p3.md

Problem

Problem 3-2: Relative asymptotic growths
Indicate, for each pair of expressions (A, B) in the table below, whether A is O, o, Ω, ω, or Θ of B. Assume that k ≥ 1, ε > 0, and c > 1 are constants. Your answer should be in the form of the table with "yes" or "no" written in each box.

A	B	O	o	Ω	ω	Θ

Solution

A	B	O	o	Ω	ω	Θ
		yes	yes	no	no	no

1. 
2. 
   • L'Hôpital's rule

A	B	O	o	Ω	ω	Θ
		yes	yes	no	no	no

A	B	O	o	Ω	ω	Θ
		no	no	no	no	no

A	B	O	o	Ω	ω	Θ
		no	no	yes	yes	no

A	B	O	o	Ω	ω	Θ
		no	no	yes	yes	no

A	B	O	o	Ω	ω	Θ
		yes	no	yes	no	yes

1. 
   • 夾擠
2. 
   • 斯特靈公式