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
I answered a) in my test
if the limit is zero, the denominator is much greater than the numerator, right?
right?
f(x) must grow slower than g(x) to be zero so the answer is A
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