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Today's Calculation Of Integral
2007 Today's Calculation Of Integral
219
219
Part of
2007 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 219
Source: Kochi University entrance exam/Medical 2007
8/28/2007
Let f(x)\equal{}\left(1\plus{}\frac{1}{x}\right)^{x}\ (x>0). Find
lim
n
→
∞
{
f
(
1
n
)
f
(
2
n
)
f
(
3
n
)
⋯
⋯
f
(
n
n
)
}
1
n
\lim_{n\to\infty}\left\{f\left(\frac{1}{n}\right)f\left(\frac{2}{n}\right)f\left(\frac{3}{n}\right)\cdots\cdots f\left(\frac{n}{n}\right)\right\}^{\frac{1}{n}}
lim
n
→
∞
{
f
(
n
1
)
f
(
n
2
)
f
(
n
3
)
⋯⋯
f
(
n
n
)
}
n
1
.
calculus
integration
limit
algebra
function
domain
logarithms