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

Question

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

e. x^3 - x^2

Accepted Answer

Welcome back everyone. As x approaches infinity, which function, if any, grows faster? F of x equals x the power of 4 minus x cubed, or g x equals x cubed. A f of x, b g of x. C, they grow at the same rate, and d cannot be determined. Let's remember that to compare the growth rate of two functions, we basically want to find the limit as x approaches infinity of their ratio. We can take f of x in the numerator and g of x in the denominator. This gives us a limit of. F of x which is x the power of 4 minus x cubed divided by g of x which is x cubed s x approaches infinity. So now to calculate this limit, we can simply factor out x cubed in the numerator. We get limit as x approaches infinity of x cubed in parentheses x minus 1 in the denominator we have x cubed. And this allows us to cancel out x cubed. So we are simply evaluating the limit as x approaches infinity of x minus 1. And this gives us infinity minus 1. Which is basically an infinitely large number. So we got a limit of infinity, and whenever we get a limit of infinity, it basically means that the numerator function dominates over the denominator function and therefore it grows faster. So in this case, our numerator function is f x, and the answer corresponds to the answer choice A F x grows faster than G of X. Thank you for watching.

4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?e. x^3 - x^2

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4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?
e. x^3 - x^2