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What is the minimum and maximum value of the function x/(ln(x!))?Please explain the answer.

What is the minimum and maximum value of the function x/(ln(x!))?Please explain the answer.

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
The factorial is defined on natural numbers only; integration is for real functions (or extensions thereof with Lebesgue theory). Nevertheless, there are three generalizations that can make your question meaningful:
  • Expand the factorial to 0 for values outside its domain (this is standard). Then the integral
  • Integration can be seen as a continuous analogue to simple summation, so it would not be unreasonable to offer summation as an alternative solution to the question. The factorial sum function is documented, but cannot be written nicely in terms of high school functions.

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