Video Transcript
If the limit of 𝑓 of 𝑥 over 𝑔 of
𝑥 as 𝑥 approaches ∞ is ∞, what do you notice about the growth rate
of 𝑓 of 𝑥 compared to 𝑔 of 𝑥 as 𝑥 approaches ∞?
This limit tells us that the
quotient 𝑓 of 𝑥 over 𝑔 of 𝑥 grows without bound as 𝑥 approaches ∞. And for the quotient 𝑓 of 𝑥 over
𝑔 of 𝑥 to grow without bound, the function 𝑓 of 𝑥 must be growing faster than 𝑔
of 𝑥. Our conclusion is, therefore, that
the growth rate of 𝑓 of 𝑥 is greater than that of 𝑔 of 𝑥 as 𝑥 approaches
∞. Another way of saying this is that
the function 𝑓 of 𝑥 dominates the function 𝑔 of 𝑥.
