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Problem
Problem
Let
f
:
R
→
R
f: R \to R
f
:
R
→
R
be such that
f
(
1
)
=
3
f(1) = 3
f
(
1
)
=
3
and
f
′
(
1
)
=
6
f'(1) = 6
f
′
(
1
)
=
6
. Then,
lim
x
→
0
[
f
(
1
+
x
)
f
(
1
)
]
1
/
x
\lim_{x \to 0} \left[ \frac{f(1+x)}{f(1)} \right]^{1/x}
lim
x
→
0
[
f
(
1
)
f
(
1
+
x
)
]
1/
x
equals a. 1 b.
e
2
e^2
e
2
c.
e
3
e^3
e
3
d.
e
4
e^4
e
4
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