Many Calculators or Computers Cannot Directly Calculate 70 ! or Higher

question 34

Multiple Choice

Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm{n}$ is large, $\mathrm{n}$ ! can be approximated by $\mathrm{n} !=10^{\mathrm{K}}$ , where $\mathrm{K}=(\mathrm{n}+0.5) \log n+0.39908993-0.43429448 \mathrm{n}$ . Evaluate 79 ! using the approximation given above.

• A) \( 8.937 \times 10^{116} \)
• B) \( 1.005 \times 10^{116} \)
• C) \( 2.890 \times 10^{313} \)
• D) \( 1.170 \times 10^{2} \)

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