Consider f(x) = x(ln x)² and g(x) = x^1.5

a) Graph the two functions together on Desmos ( Links to an external site.). Click on the wrench (settings) icon so you can set the maximum x value to 45 and the maximum y value to 2000. Then upload a screenshot of your graphs.

b) From Part a, you probably noticed that f(x) appears to grow more quickly than g(x). In fact the opposite is true asymptotically, since lim(f(x) /g(x)) = 0 as x goes to infinity.

Prove this result by taking the limit and using L'Hpital's rule (more than once).

c) Repeat part a, but this time use 8000 for the maximum x value and 500,000 for the maximum y value. (This should help explain the result in Part b.)