Question
Give Stirling's approximation and outline its significance. Calculate the % error introduced in computing the value of 10! by using this approximation. (Given In 2=0.69 and In 3= 1.01)
Answer :
Word Count : 395
### Stirling’s Approximation: Stirling's approximation for factorials is given by: \[ n! \approx \sqrt{2\pi n} \left( \frac{n}{e} \right)^n \] where \( e \) is the base of the natural logarithm (\( e \approx 2.718 \)). ### Significance of Stirling's Approximation: - It provides an asymptotic estimate for large values of \( n \). - It simplifies factorial calculations, which grow rapidly. - It is useful ___ __________ ___ ______ ___ ________ ______.
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### Stirling’s Approximation: Stirling's approximation for factorials is given by: \[ n! \approx \sqrt{2\pi n} \left( \frac{n}{e} \right)^n \] where \( e \) is the base of the natural logarithm (\( e \approx 2.718 \)). ### Significance of Stirling's Approximation: - It provides an asymptotic estimate for large values of \( n \). - It simplifies factorial calculations, which grow rapidly. - It is useful ___ __________ ___ ______ ___ ________ ______.
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