- #1

Goldenwind

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## Homework Statement

These are some problems I need to solve. Do not solve them for me. I ask two things from you:

1) Explain what the question is asking from me, as I'm a little unclear on this.

2) Using a completely unrelated example, or whichever not-doing-it-for-me method you wish, give a hint as to how I might actually be able to do these.

Question 1: Find the least integer n such that f(x) is O(x^n) for each of these functions.

a) f(x) = 2x^2 + x^3 * log(x)

b) f(x) = 3x^5 + (log(x))^4

c) f(x) = (x^4 + x^2 + 1) / (x^4 + 1)

d) f(x) = (x^3 + 5log(x)) / (x^4 + 1)Question 2: Give a big-O estimate for each of these functions. For the function g in your estimate that f(x) is O(g(x)), use a simple function g of the smallest order.

a) nlog(n^2 + 1) + n^2 * log(n)

b) (nlog(n) + 1)^2 + (log(n) + 1)(n^2 + 1)

c) n^(2^n) + n^(n^2)

## Homework Equations

1, logn, n, nlogn, n^2, 2^n and n! are the "often used" terms.

## The Attempt at a Solution

I read the textbook. My problem might be as simple as not understanding what they're asking, but totally knowing how to do it, or maybe I don't understand it anyway... I can't really gauge that until I figure out what they want :P

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