Evaluate the limit _ x x- x^ 2 +1 ! ( 1 x )

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Evaluate the limit lim⁡x→∞x−x2+1sin⁡ ⁣(1x).\lim_{x\to\infty}\frac{x-\sqrt{x^{2}+1}}{\sin\!\left(\dfrac{1}{x}\right)}. Give your answer as a simplified real number.

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