# mid1review - CMPS 101 Midterm 1 Review Problems 1 Let n f...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CMPS 101 Midterm 1 Review Problems 1. Let ) ( n f and ) ( n g be asymptotically non-negative functions which are defined on the positive integers. a. State the definition of )) ( ( ) ( n g O n f = . b. State the definition of )) ( ( ) ( n g n f ω = 2. State whether the following assertions are true or false. If any statements are false, give a related statement which is true. a. )) ( ( ) ( n g O n f = implies )) ( ( ) ( n g o n f = . b. )) ( ( ) ( n g O n f = if and only if )) ( ( ) ( n f n g Ω = . c. )) ( ( ) ( n g n f Θ = if and only if L n g n f n = ∞ → )) ( / ) ( ( lim , where ∞ < < L . 3. Prove that )) ( ) ( ( )) ( ( )) ( ( n g n f n g n f ⋅ Θ = Θ ⋅ Θ . In other words, if )) ( ( ) ( 1 n f n h Θ = and )) ( ( ) ( 2 n g n h Θ = , then )) ( ) ( ( ) ( ) ( 2 1 n g n f n h n h ⋅ Θ = ⋅ . 4. Use limits to prove the following (these are some of the exercises at the end of the asymptotic growth rates handout): a. If ) ( n P is a polynomial of degree ≥ k , then ) ( ) (...
View Full Document

## This note was uploaded on 12/03/2009 for the course CS CS101 taught by Professor Agoreback during the Spring '09 term at American College of Gastroenterology.

### Page1 / 2

mid1review - CMPS 101 Midterm 1 Review Problems 1 Let n f...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online