Determinate forms

When both limits are finite, operations on limits follow the natural rules of algebra.

In summary — Rule 1: determinate forms

If $\lim f(x) = a$ and $\lim g(x) = b$ (both finite), then:

• $\lim(f+g) = a+b$,   $\lim(f\cdot g) = ab$,   $\lim(f/g) = a/b$ if $b\ne 0$;
• $\lim f^{\,g} = a^{\,b}$ if $a>0$.

In all these cases the limit is computed “directly”, by substituting the limit values of the individual functions.

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Topics: Limits
Concepts: Determinate forms · Limit
Skills: Using formulae