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Here is the problem: (3x squared plus 1)/(x squared minus 2).

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Find the limit of (3 x squared plus 1) / (x squared minus 2) as x → ∞.

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Indeterminate form ∞/∞ — apply L prime Hôpital prime s rule. Differentiate the numerator and the denominator separately (this is not the quotient rule).

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Simplify.

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The expression is constant.

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So the answer is Limit equals 3.

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A limit describes the value a function approaches, not necessarily the value it takes. When substitution gives an indeterminate form, the expression is rewritten (L prime Hôpital prime s rule, a conjugate, or logarithms) until substitution works.

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Numerical values as x grows agree: f(127.18281) equals 3.0004328, f(1271.8281) equals 3.0000043, f(12718.281) equals 3, f(127182.81) equals 3, which checks out.