How do you evaluate limits in calculus?

March 6, 2026Languages

ScanSolve AI Answer

March 6, 2026

Answer

lim(x→2) (x+2)(x-2)/(x-2) = lim(x→2) (x+2) = 4.

A limit describes what value f(x) approaches as x approaches some value. Methods: 1) Direct substitution — plug in the value. 2) Factoring — if you get 0/0, factor and cancel. 3) L'Hôpital's Rule — if 0/0 or ∞/∞, take derivatives of top and bottom. 4) Rationalization — multiply by conjugate for roots. Example: lim(x→2) (x²-4)/(x-2) = lim(x→2) (x+2)(x-2)/(x-2) = lim(x→2) (x+2) = 4.

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Quick Answer

A limit describes what value f(x) approaches as x approaches some value.
Methods: 1) Direct substitution — plug in the value.
2) Factoring — if you get 0/0, factor and cancel.
3) L'Hôpital's Rule — if 0/0 or ∞/∞, take derivatives of top and bottom.

Asked on March 6, 2026Languages

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ScanSolve AI AnswerAnswered on March 6, 2026

A limit describes what value f(x) approaches as x approaches some value. Methods: 1) Direct substitution — plug in the value. 2) Factoring — if you get 0/0, factor and cancel. 3) L'Hôpital's Rule — if 0/0 or ∞/∞, take derivatives of top and bottom. 4) Rationalization — multiply by conjugate for roots. Example: lim(x→2) (x²-4)/(x-2) = lim(x→2) (x+2)(x-2)/(x-2) = lim(x→2) (x+2) = 4.