2.1, due on September 26

Reflective:
One question I had was, why is it important to find the analytic bounds on the big-O of a function? For example, Example 2.1.2 shows that 22,026! is between 198,235 and 198, 245, which "isn't good enough." Why can we not just compute 22,026!? Is is more difficult to compute factorials than the analytic expressions that bound them?

Difficult:
Yep, the proof of Stirling's approximation got me. In fact, I had a hard time understanding the very first part. How is nlog(n) - n + 1 = integral_0^n(log(x)dx? It seems like the integral should evaluate to log(n) - log(1) = log(n).

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