Need help ASAP please! Due tonight :( LIMITS CALCULUS

Question

What does  show? (4 points)

Answer Choices

	g(x) grows faster than f(x) as x goes to infinity.
	f(x) and g(x) grow at the same rate as x goes to infinity.
	f(x) grows faster than g(x) as x goes to infinity.
	L'Hôpital's Rule must be used to determine the true limit value

Answer 1

f(x) grows faster than g(x) as x goes to infinity is the correct answer.

Best way to think of the problem is by using sample functions. let f(x)= e^x and g(x)=x

We know that e^x grows much faster than x by trying trying a few values. Let's try x=1,10,100

e¹=2.718 , e¹⁰=22026 , e¹⁰⁰=2.688X10⁴³

so 2.718 / 1 = 2.718

and 22026 / 10 = 2020.6

and (2.688X10^43) / 100 = 2.688X10^41

Notice since e^x is growing so much faster that when you divide the functions your solution is getting bigger and bigger and headed toward positive infinity for your y value as x goes to infinity