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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.
  • 2 worked examples
  • 18 in Limits & Continuity

Worked examples

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

Answer: 45

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Find lim(x→0) 7 sin(x).

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Common questions

What is the Limit of a Constant Multiple?

A constant factor can be pulled out of a limit. It is one of the limits & continuity formulas in the CalcRef reference.

When does the Limit of a Constant Multiple apply?

The Limit of a Constant Multiple holds under this condition: lim f(x) must exist and c is a constant.

How do you use the Limit of a Constant Multiple?

Worked example. Find lim(x→3) 5x². 5 · lim(x→3) x² = 5 · 9. Answer: 45.

Practice

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