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Problems
Let
f
(
x
)
=
(
1
+
1
x
)
x
(
x
>
0
)
and
\text{Let } f(x) = \left(1 + \frac{1}{x}\right)^x \quad (x > 0) \text{ and}
Let
f
(
x
)
=
(
1
+
x
1
)
x
(
x
>
0
)
and
g
(
x
)
=
{
x
ln
(
1
+
(
1
/
x
)
)
,
if
0
<
x
≤
1
0
,
if
x
=
0
g(x) = \begin{cases} x \ln(1 + (1/x)), & \text{if } 0 < x \le 1 \\ 0, & \text{if } x = 0 \end{cases}
g
(
x
)
=
{
x
ln
(
1
+
(
1/
x
))
,
0
,
if
0
<
x
≤
1
if
x
=
0
…
Problem
Let
f
(
x
)
=
(
1
+
1
x
)
x
(
x
>
0
)
and
\text{Let } f(x) = \left(1 + \frac{1}{x}\right)^x \quad (x > 0) \text{ and}
Let
f
(
x
)
=
(
1
+
x
1
)
x
(
x
>
0
)
and
g
(
x
)
=
{
x
ln
(
1
+
(
1
/
x
)
)
,
if
0
<
x
≤
1
0
,
if
x
=
0
g(x) = \begin{cases} x \ln(1 + (1/x)), & \text{if } 0 < x \le 1 \\ 0, & \text{if } x = 0 \end{cases}
g
(
x
)
=
{
x
ln
(
1
+
(
1/
x
))
,
0
,
if
0
<
x
≤
1
if
x
=
0
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) \cdot f\left(\frac{2}{n}\right) \cdot f\left(\frac{3}{n}\right) \dots f\left(\frac{n}{n}\right) \right\}^{1/n}
lim
n
→
∞
{
f
(
n
1
)
⋅
f
(
n
2
)
⋅
f
(
n
3
)
…
f
(
n
n
)
}
1/
n
equals a.
2
e
\sqrt{2}e
2
e
b.
2
e
\sqrt{2e}
2
e
c.
2
e
2\sqrt{e}
2
e
d.
e
\sqrt{e}
e
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