1. Which of the following functions grow faster than e^x as x→...

Question

1. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?

f. (e^x)/2

Accepted Answer

Welcome back, everyone. Determine whether the function F of X equals eats the power of x + 3, grows faster than eats the power of X as X approaches infinity. A says F of X grows slower than eats the power of X. B F of X grows faster than eats the power of X. C. They grow at the same rate, and D cannot be determined. For this problem, let's remember that we can compare growth rate of two functions if we take the limit of their ratio as x approaches infinity. What we can do is simply take F of X in the numerator and G of X in the denominator. So we are going to evaluate the limit as X approaches infinity of E to the power of X + 3 divided by E to the power of X. And to evaluate this limit, we can use the properties of exponents. We can rewrite our numerators it to the power of X multiplied by E cubed, and we're dividing by e to the power of X. Notice that the power of X can be canceled out and we're taking the limit of a constant which gives us a constant. Because we got a constant that is not equal to 0, we can conclude that F and G grow at the same rate, right? This is by definition if we get a limit of the ratio that is a constant, not equal to 0, the growth rate is the same. So we can conclude that the correct answer is option C. They grow at the same rate. Thank you for watching.

1. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?f. (e^x)/2

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1. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?
f. (e^x)/2