Limits and their Properties

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Limits and their Properties by Mind Map: Limits and their Properties

1. 1.1: A Preview of Calculus

1.1. Understand what calculus is and how it compares to precalculus

1.2. Understand that the tangent line problem is basic to calculus

1.3. Understand that the area problem is also basic to calculus

2. 1.2: Finding Limits Graphically and Numerically

2.1. Estimate a limit using a numerical or graphical approach

2.2. Learn different ways that a limit can fail to exist

2.3. Study and use a formal definition of a limit

3. 1.3: Evaluating Limits Analytically

3.1. Evaluate a limit using properties of limits.

3.2. Develop and use a strategy for finding limits

3.3. Evaluate a limit using dividing out and rationalizing techniques

3.4. Evaluate a limit using the Squeeze Theorem

4. 1.4: Continuity and One-Sided Limits

4.1. Determine continuity at a point and continuity on an open interval

4.2. Determine one-sided limits and continuity on a closed interval

4.3. Use properties of continuity

4.4. Understand and use the Intermediate Value Theorem

5. 1.5: Infinite Limits

5.1. Determine infinite limits from the left and from the right.

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