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Problem
Problem
The largest value of the non-negative integer
a
a
a
for which
lim
x
→
1
{
−
a
x
+
sin
(
x
−
1
)
+
a
x
+
sin
(
x
−
1
)
−
1
}
1
−
x
1
−
x
=
1
4
\lim_{x \to 1} \left\{ \frac{-ax + \sin(x-1) + a}{x + \sin(x-1) - 1} \right\}^{\frac{1-x}{1-\sqrt{x}}} = \frac{1}{4}
lim
x
→
1
{
x
+
s
i
n
(
x
−
1
)
−
1
−
a
x
+
s
i
n
(
x
−
1
)
+
a
}
1
−
x
1
−
x
=
4
1
is
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