How do you evaluate limits in calculus?

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

This languages problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.

ScanSolve AI 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. 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.