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Overview
Calculus
1. Concept of Limits
1.2 Finding limits from graphs
Finding Limits from Graphs
A clear, visual guide to reading limits directly off a graph, including one-sided limits, jump discontinuities, and piecewise functions.
What You'll Learn
A limit from a graph is found by tracing the curve toward an x-value from both sides and checking where the outputs are heading.
A two-sided limit only exists when the left-hand limit and the right-hand limit agree at that x-value.
Open circles, closed circles, and jumps in a piecewise graph are the key visual clues for reading limits correctly.
The actual height of the function at a point (an open or closed dot) does not have to match the limit value.
Graphical limits are a visual shortcut for the same ideas used in algebraic limit techniques and continuity checks.
What You'll Practice
1
Finding left-hand and right-hand limits from piecewise graphs
2
Determining if two-sided limits exist by comparing directional approaches
3
Evaluating function values at points with hollow and solid dots
4
Analyzing graphs with discontinuities and jump behaviors
Why This Matters
Understanding limits graphically is the foundation for all of calculus. This skill helps you analyze function behavior near critical points, which is essential for studying continuity, derivatives, and integrals in advanced math courses.
This Unit Includes
5 Video lessons
Learning resources
Skills
Limits
One-Sided Limits
Two-Sided Limits
Graph Analysis
Continuity
Function Values
Calculus Foundations
IL Curriculum Aligned