Finding the Big O of polynomials

[IAmPat]

Homework Statement

1. Use the definition of "f(x) is O(g(x))" to show that 2^x + 17 is O(3^x)').
2. Determine whether the function x^4/2 is O(x^2)


2. The attempt at a solution

1. From my understanding, I would say of course 2^x + 17 is O(3^x) because the constant is of such low order that 2^x would never reach 3^x. I don't know how to prove it mathematically though.

2. To be honest, I just don't understand the steps I need to take to prove or disprove this. I have a vague understanding of big O but even with teacher examples and lots of googling, it seems like nobody knows what the hell they're talking about. I need some intuition

 

[lanedance]

how about starting with the definition of big Oh