1. 1.4 Calculating limits

2. Limit Laws Suppose that c is a constant and the limits and exist. Then

3. Limit Laws (cont.) Suppose that c is a constant, n is a positive integer and the limit exists. Then

4. Direct Substitution Property If f is a polynomial or a rational function and a is in the domain of f, then Example: More examples on the board.

5. Properties of Limits Theorem: If f(x) ≤ g(x) when x is near a (except possibly at a) and the limits of f and g both exist as x approaches a, then The Squeeze Theorem: If f(x) ≤ g(x) ≤ h(x) when x is near a (except possibly at a) and then (sometimes is called the Sandwich Theorem)

6. Show that The maximum value of sine is 1, soThe minimum value of sine is -1, soSo: By the squeeze theorem: Example: