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1.4 Calculating limits
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Limit Laws Suppose that c is a constant and the limits and exist. Then
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Limit Laws (cont.) Suppose that c is a constant, n is a positive integer and the limit exists. Then
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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.
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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)
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Show that The maximum value of sine is 1, soThe minimum value of sine is -1, soSo: By the squeeze theorem: Example:
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