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Mathematics
Mathematics
Problem
If
f
(
x
)
=
lim
t
→
0
tan
−
1
(
e
x
t
−
1
t
)
f(x) = \lim_{t \rightarrow 0} \tan^{-1} \left( \frac{e^{xt}-1}{t} \right)
f
(
x
)
=
lim
t
→
0
tan
−
1
(
t
e
x
t
−
1
)
, then
lim
x
→
0
f
(
x
)
−
x
x
3
\lim_{x \rightarrow 0} \frac{f(x)-x}{x^3}
lim
x
→
0
x
3
f
(
x
)
−
x
is equal to (a)
1
2
\frac{1}{2}
2
1
(b)
−
1
2
\frac{-1}{2}
2
−
1
(c)
1
3
\frac{1}{3}
3
1
(d)
−
1
3
\frac{-1}{3}
3
−
1
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