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Mathematics
Problem
Evaluate the limit
lim
x
→
∞
x
−
x
2
+
1
sin
(
1
x
)
.
\lim_{x\to\infty}\frac{x-\sqrt{x^{2}+1}}{\sin\!\left(\dfrac{1}{x}\right)}.
x
→
∞
lim
sin
(
x
1
)
x
−
x
2
+
1
.
Give your answer as a simplified real number.
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