Factorisation

In $0/0$ forms with polynomial expressions (or ones reducible to polynomials), the typical approach is to factorise the numerator and denominator so as to bring out — and then cancel — the factor that vanishes.

Example — Factorisation ( $0/0$ form)

$\lim_{x\to 2}\frac{x^2-4}{x-2} = \lim_{x\to 2}\frac{(x-2)(x+2)}{x-2} = \lim_{x\to 2}(x+2) = 4.$

The factor $(x-2)$, responsible for the $0/0$ form, appears both above and below: after cancelling, a continuous expression remains, into which it suffices to substitute $x=2$.

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Topics: Limits
Concepts: Indeterminate forms
Skills: Calculating limits · Factorising