The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
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Which function is bigger: n^n , n! , e^n , n^100 , ln(n) ? As n becomes large, all of these functions (or sequences, if you prefer) diverge to infinity. But some of them grow larger faster than others. We often think of exponentials as extremely fast growing, and they are, but they are actually slower than factorials and n to the exponent n. And all of those are faster than any polynomial like a quadratic and those are all faster then logarithms. We will state the big theorem for limits, see how to apply this theorem, and then prove the different limits involved.
0:00 The Hierarchy of Functions
1:02 Graphing the Functions with Maple Learn
2:57 The Big Theorem
4:40 Applying the Big Theorem
8:44 Proving that n^n beats n!
10:20 Proving that polynomials beat logarithms
11:49 Proving that factorials beat exponentials
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