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Limits and their Properties
by Scott Hopkins
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Limits and their Properties

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1.1: A Preview of Calculus

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Understand what calculus is and how it compares to precalculus

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Understand that the tangent line problem is basic to calculus

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Understand that the area problem is also basic to calculus

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1.2: Finding Limits Graphically and Numerically

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Estimate a limit using a numerical or graphical approach

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Learn different ways that a limit can fail to exist

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Study and use a formal definition of a limit

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1.3: Evaluating Limits Analytically

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Evaluate a limit using properties of limits.

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Develop and use a strategy for finding limits

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Evaluate a limit using dividing out and rationalizing techniques

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Evaluate a limit using the Squeeze Theorem

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1.4: Continuity and One-Sided Limits

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Determine continuity at a point and continuity on an open interval

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Determine one-sided limits and continuity on a closed interval

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Use properties of continuity

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Understand and use the Intermediate Value Theorem

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1.5: Infinite Limits

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Determine infinite limits from the left and from the right.

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Find and sketch the vertical asymptotes of the graph of a function

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