CalcRef

Limits & Continuity · Limit Laws

Limit of a Constant Multiple

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

A constant factor can be pulled out of a limit.

Conditions. lim f(x) must exist and c is a constant.

Worked examples

Find lim(x→3) 5x².
  1. 5 · lim(x→3) x² = 5 · 9

Answer: 45

Find lim(x→0) 7 sin(x).
  1. 7 · lim(x→0) sin(x) = 7 · 0

Answer: 0

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