Stirling's formula (named after Scottish mathematician, James Stirling: 1692-1770) is used to
approximate large values of n!. Stirling's formula is $n ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }$ a. Use Stirling's formula to approximate the given expression. Round to the nearest whole unit.
b. Compute the actual value of the expression.
-$8 !$
A) a. 39,902
b. 40,312
B) a. 40,111
b. 40,320
C) a. 40,111
b. 40,312
D) a. 39,902
b. 40,320

Question

Quizplus · Accepted Answer

Stirling's formula approximation for $8!$ is $\sqrt{2\pi \times 8} \left(\frac{8}{e}\right)^8 \approx 39,902$ when rounded to the nearest whole number. The actual value of $8!$ is $8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320$.

Stirling's Formula (Named After Scottish Mathematician, James Stirling: 1692-1770) Is n!≈2πn(ne)nn ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }n!≈2πn​(en​)n

Stirling's Formula (Named After Scottish Mathematician, James Stirling: 1692-1770) Is $n ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }$