Chapter 16.5
Infinite Limits and Vertical Asymptotes
Gain a deep understanding of infinite limits and vertical asymptotes, essential concepts in calculus. Our comprehensive guide provides video tutorials, examples, and practice problems.
What You'll Learn
Identify infinite limits as x approaches vertical asymptotes from both directions
Determine whether a function approaches positive or negative infinity using one-sided limits
Recognize that vertical asymptotes occur where infinite limits exist
Distinguish between vertical asymptotes and removable discontinuities (holes)
Apply numerical analysis to evaluate limits near domain restrictions
What You'll Practice
1
Finding left-hand and right-hand limits as x approaches vertical asymptotes
2
Evaluating limits graphically by analyzing function behavior near discontinuities
3
Using sign analysis to determine if limits approach positive or negative infinity
4
Identifying vertical asymptotes and holes in rational functions
Why This Matters
Understanding infinite limits and vertical asymptotes is essential for analyzing rational functions and their graphs. This concept appears throughout calculus when studying continuity, derivatives, and curve sketching, and helps you predict function behavior near undefined points.
This Unit Includes
11 Video lessons
Practice exercises
Learning resources
Skills
Infinite Limits
Vertical Asymptotes
One-Sided Limits
Rational Functions
Domain Restrictions
Discontinuities
Numerical Analysis
