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Limits and their Properties by
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# Limits and their Properties

## 1.1: A Preview of Calculus

Understand what calculus is and how it compares to precalculus

Understand that the tangent line problem is basic to calculus

Understand that the area problem is also basic to calculus

## 1.2: Finding Limits Graphically and Numerically

Estimate a limit using a numerical or graphical approach

Learn different ways that a limit can fail to exist

Study and use a formal definition of a limit

## 1.3: Evaluating Limits Analytically

Evaluate a limit using properties of limits.

Develop and use a strategy for finding limits

Evaluate a limit using dividing out and rationalizing techniques

Evaluate a limit using the Squeeze Theorem

## 1.4: Continuity and One-Sided Limits

Determine continuity at a point and continuity on an open interval

Determine one-sided limits and continuity on a closed interval

Use properties of continuity

Understand and use the Intermediate Value Theorem

## 1.5: Infinite Limits

Determine infinite limits from the left and from the right.

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