3. Which of the following functions grow faster than x² as x→∞...

Question

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

a. x² + 4x

Accepted Answer

Welcome back everyone. As X approaches infinity, which function, if any, grows faster. F of X equals XL and X or G of X equals X. A says F of X. B G of X. C they grow at the same rate, and D cannot be determined. For this problem, let's remember that if we want to compare the growth rates of two functions, we're going to take the limit as X approaches infinity of their ratio. We're going to take the limit as X approaches infinity of G of X divided by F of X, even though we can swap them, we can take F in the numerator and G in the denominator. The outcome will be interpreted accordingly. So, let's substitute each function. We're going to get limit as X approaches infinity of X divided by XL and X. And notice that we can cancel out Xs. To get limit. As x approaches infinity of 1 divided by LN of X. So now in the numerator, we have a constant which is 1, and as X approaches infinity, a line of X also approaches infinity. Whenever we divide a constant by an infinitely large number, we get a limit of 0. And now we're going to interpret it. So, if we get a limit of 0, it basically means that the denominator function grows faster because it dominates over the numerator function, right? Therefore, we can conclude that F of X. Gross Faster And the correct answer for this problem corresponds to the answer choice A. Thank you for watching.

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?a. x² + 4x

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3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?
a. x² + 4x