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Limit Laws

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Limit Laws

$lim_{x \to a} (f (x) \pm g (x)) = lim_{x \to a} f (x) \pm lim_{x \to a} g (x)$ $lim_{x \to a} c \cdot f (x) = c \cdot lim_{x \to a} f (x)$

$lim_{x \to a} = \frac{{lim}_{x \to a} f (x)}{{lim}_{x \to a} g (x)}$ $lim_{x \to a} f (x) \cdot g (x) = lim_{x \to a} f (x) \cdot lim_{x \to a} g (x)$

$lim_{x \to a} {(f (x))}^{n} = {(lim_{x \to a} f (x))}^{n}$ $lim_{x \to a} f (g (x)) = f (lim_{x \to a} g (x))$

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Chapter 2 - Continuity and Limits

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Limit laws
Limit laws allow limits of sums, products, and suitable quotients to be assembled from the limits of their parts. The component limits must exist as required, and a quotient law needs a nonzero denominator limit. For example, if f approaches 2 and g approaches 3, then f+g approaches 5 and fg approaches 6. Direct substitution into a quotient with denominator limit 0 is not justified by the quotient limit law.
Read more: 1.5 · Algebraic properties of limits →

Limit laws

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