# Basic Limit Laws - PowerPoint PPT Presentation

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Basic Limit Laws. 2.3. Theorem 1: Basic Limit Laws. If lim x →c f(x) and lim x→c g(x) exist, then Sum Law: lim x→c (f(x) + g(x)) exists and lim x→c (f(x) + g(x)) = lim x→c f(x) + lim x→c g(x).

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Basic Limit Laws

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## Basic Limit Laws

2.3

### Theorem 1: Basic Limit Laws

If lim x→c f(x) and lim x→c g(x) exist, then

• Sum Law: lim x→c (f(x) + g(x)) exists and lim x→c (f(x) + g(x)) = lim x→c f(x) + lim x→c g(x).

• Constant Multiple Law: For any number k, lim x→c kf(x) exists and lim x→c kf(x) = k lim x→c f(x).

• Product Law: lim x→c f(x)g(x) exists and lim x→c f(x)g(x) = (lim x→c f(x))(lim x→c g(x)).

### Theorem 1 Continued

• Quotient Law: If lim x→c g(x) ≠ 0, then lim x→c f(x)/g(x) exists and lim x→c f(x)/g(x) = lim x→c f(x)

lim x→c g(x).

• Powers & Roots: if p, q are integers with q ≠ 0, then limx→c exists and it equals . Assume that lim x→c f(x) ≥ 0 if q is even, and that lim x→c ≠ 0 if p/q < 0. In particular for n a positive integer, limx→c [f(x)]n = (lim x→c f(x))n and

### Example 1

• lim x→4 x2 + 2x – 7

• lim x→-1

Substitution can be used to evaluate limits when the function is continuous.