japplepie said:How do I solve for x in the relationship below:
nx ~ n ln(n), as n -> infinity
The answer that I'm getting is x=1, but that must be wrong since 1 ~ ln(n) as n-> infinity is wrong.
To identify the asymptotic equality, you need to look at the growth rate of the functions involved. If the functions have the same growth rate as the input size increases, then they are asymptotically equal.
The most common techniques for solving asymptotic equalities are using limit calculus, algebraic manipulation, and using the definition of asymptotic notation.
No, limits are essential for solving asymptotic equalities as they help to determine the growth rate of a function as the input size approaches infinity.
To prove that two functions are asymptotically equal, you need to show that their ratio approaches 1 as the input size increases. This can be done using the limit definition of asymptotic notation.
Yes, there is a difference. Asymptotic equality means that the two functions have the same growth rate, while asymptotic equivalence means that they have the same growth rate and differ only by a constant factor.