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Limits & Continuity · Limit Laws

Limit of a Sum

lim⁡x→a[f(x)+g(x)]=lim⁡x→af(x)+lim⁡x→ag(x)\lim_{x \to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)

The limit of a sum equals the sum of the limits, provided both limits exist.

Conditions. Both lim f(x) and lim g(x) must exist.

Worked examples

Find lim(x→2) (x² + 3x).
  1. lim(x→2) x² + lim(x→2) 3x
  2. = 4 + 6

Answer: 10

Find lim(x→0) (sin x + x).
  1. lim(x→0) sin x + lim(x→0) x = 0 + 0

Answer: 0

Related formulas

Limit of a ProductLimit of a Quotient

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