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Limits and their Properties
by Scott Hopkins
# Limits and their Properties

## 1.1: A Preview of Calculus

## 1.2: Finding Limits
Graphically and Numerically

## 1.3: Evaluating Limits Analytically

## 1.4: Continuity and One-Sided Limits

## 1.5: Infinite Limits

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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

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

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

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

Determine infinite limits from the left and from the right.

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