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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
x
→
0
+
g
(
x
)
\lim_{x \to 0^+} g(x)
lim
x
→
0
+
g
(
x
)
a. is equal to 0 b. is equal to 1 c. is equal to
e
e
e
d. is non-existent
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