lim
x
→
1
2
⋅
ln
(
x
)
e
x
−
1
\lim \limits_{x \to 1} \dfrac{2\cdot \ln(x)}{e^x-1}
x
→
1
lim
e
x
−
1
2
⋅
ln
(
x
)
2
e
\dfrac{2}{e}
e
2
1
1
1
0
0
0
nonexistent
Summary
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Approach
lim
x
→
1
2
⋅
ln
(
x
)
e
x
−
1
\lim \limits_{x \to 1} \frac{2\cdot \ln(x)}{e^x-1}
x
→
1
lim
e
x
−
1
2
⋅
ln
(
x
)
=
2
ln
(
1
)
e
1
−
1
= \frac{2\ln(1)}{e^1-1}
=
e
1
−
1
2
ln
(
1
)
=
2
(
0
)
e
−
1
= \frac{2(0)}{e-1}
=
e
−
1
2
(
0
)
=
0
e
−
1
= \frac{0}{e-1}
=
e
−
1
0
=
0
= \boxed{0}
=
0