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[✓] Determine if a function is Big-O ?

GROUPS:

Greetings,

Is anyone familiar using Wolfram Mathematica to determine whether a function is a big-O as per example below:

To establish a big-O relationship, find witnesses C and k such that |f(x)| <= C|g(x)| whenever x>k.
Determine whether the function is O(x^2).
f(x) = 17x + 11

The solution should be "Yes", because the determining factor in f(x) is less than or equal to x^2. I would like to use Mathematica to check my answer. What should my input looks like? Thanks

POSTED BY: Cael G
Answer
4 months ago

You can calculate the limit of the ratio, which should work in most cases:

If[Abs[Limit[(17 x + 11)/x^2, x -> Infinity]] < Infinity,
 True, False]
POSTED BY: Gianluca Gorni
Answer
4 months ago

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