9. True, or false? As x→∞,
a. x = o(x)

Question

9. True, or false? As x→∞,

a. x = o(x)

Accepted Answer

Welcome back, everyone. True or false, as X approaches infinity, X is equal to little O of X multiplied by LN X. A says true, and Bs says false. For this problem, let's remember the definition of little O, and specifically, if we have a form of F of X is equal to a little O of G of X. As x approaches infinity, it basically means that the limit as x approaches infinity of F of X divided by G of X is equal to 0, or basically G of X grows faster than F of X, right? Let's identify the functions that we have. Our F of X is equal to X, and G of X is equal to x multiplied by LN X. So we want to check if this limit, specifically the limit as X approaches infinity of X divided by X multiplied by LN of X. It is equal to 0. If it is equal to 0, the statement is true, right. So let's simplify. We can cross out X, and we're basically evaluating the limit as X approaches infinity of 1 divided by LN of X. In the numerator, we have a constant. And our denominator approaches infinity as x approaches infinity because we have a line of X, so one divided by an infinitely large number is going to give us a limit of 0, right, meaning since the limit is equal to 0, it basically matches the definition and the statement is true. The answer is A. Thank you for watching.

9. True, or false? As x→∞,a. x = o(x)

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9. True, or false? As x→∞,
a. x = o(x)