CalcRef

Limits & Continuity · Limit Laws

Limit of a Product

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

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

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

Worked examples

Find lim(x→3) x · (x+1).
  1. lim(x→3) x · lim(x→3) (x+1) = 3 · 4

Answer: 12

Find lim(x→1) (2x)(x²).
  1. lim(x→1) 2x · lim(x→1) x² = 2 · 1

Answer: 2

Related formulas

Limit of a SumLimit of a Quotient

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