# Limits and their Properties

# Limits and their Properties

by Scott Hopkins
# 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