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The value of the limit lim x tend to infinity gamma (x+1)/(x/e)^x√x is A. √2π. B. 1/2. C. 1/2π. D. √π/2.?
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The value of the limit lim x tend to infinity gamma (x+1)/(x/e)^x√x is...
Explanation:

Given Limit:
lim x → ∞ (gamma(x+1) / (x/e)^x * √x)

Using Stirling's approximation for gamma function:
gamma(x+1) ≈ √(2πx) * (x/e)^x

Substitute the approximation into the limit:
lim x → ∞ (√(2πx) * (x/e)^x / (x/e)^x * √x)
= lim x → ∞ √(2πx) / √x
= lim x → ∞ √(2π)
= √(2π)
Therefore, the value of the limit is √(2π) (Option A).
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The value of the limit lim x tend to infinity gamma (x+1)/(x/e)^x√x is A. √2π. B. 1/2. C. 1/2π. D. √π/2.?
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