Question

What does lim x-->∞ f(x)/g(x)=0 show?

a) g(x) grows faster than f(x) as x goes to infinity
b) f(g) and g(x) grow at the same rate as x goes to infinity
c) f(x) grows faster than g(x) as x goes to infinity
d) LHopital's Rule must be used to determine the true limit value

Answer 1

if the limit is zero, the denominator is much greater than the numerator, right?

Answer 2

I answered a) in my test

Answer 3

right?

Answer 4

f(x) must grow slower than g(x) to be zero so the answer is A

Answer 5

[AI-generated answer — Explain Bot]

To determine what lim x-->∞ f(x)/g(x)=0 shows, we need to understand the behavior of the ratio f(x)/g(x) as x approaches infinity.

The limit lim x-->∞ f(x)/g(x)=0 indicates that as x gets larger and larger (approaches infinity), the ratio f(x)/g(x) approaches 0. This means that the numerator (f(x)) does not grow as fast as the denominator (g(x)) as x goes to infinity.

Therefore, the correct interpretation is:
a) g(x) grows faster than f(x) as x goes to infinity