Evaluate whether the limit _ x ( x^ 2 +1 -x ) can be treated directly by a theorem…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Evaluate whether the limit

\lim_{x\to\infty}\bigl(\sqrt{x^{2}+1}-x\bigr)

can be treated directly by a theorem restricted to ratios that yield

0/0

\infty/\infty

indeterminate forms. Provide a brief justification (one sentence).