Here's why 2 | Desmos

Expression 3: natural log left parenthesis, 2 to the negative 48th power times "x" ! , right parenthesis

3

Error of Stirling's approximation, just for fun :)

4

Expression 5: natural log left parenthesis, "x" ! minus StartRoot, 2 pi "x" , EndRoot left parenthesis, StartFraction, "x" Over "e" , EndFraction , right parenthesis Superscript, "x" , Baseline , right parenthesis

5

6

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