Calculus I · Limits and Continuity · lesson
How to Read Limits From a Graph
Learn How to Read Limits From a Graph with plain-language explanations, guided examples, worked homework methods, interactive checks, and exam-style practice.
Where this chapter fits
Chapter 1: What a limit means
Build the neighborhood idea with motion, tables, holes, one-sided behavior, and graphs.
Reading lens: What are nearby outputs doing as the input approaches the target from both sides? Keep that question in view while reading How to Read Limits From a Graph; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects When a Limit Does Not Exist to Direct Substitution for Limits. Read the explanation first, predict each example’s next move, and only then compare the written solution.
A Reliable Method for Reading a Graph
Graph questions are often rushed and surprisingly easy to misread. At each marked input , use the same order.
Graph-Reading Routine
• Trace the curve toward from the left. Record the height approached. • Trace the curve toward from the right. Record the height approached. • Compare the one-sided limits. • Only then inspect the filled point to find .
Reading four quantities from one graph
Suppose a graph has an open circle at , the curve approaches that circle from both sides, and a filled point appears at . Find
Show worked solution
Following the curve from the left gives
Following the curve from the right gives
The two sides agree, so
The filled point gives the actual value:
Thus,
Source & rights
Original instruction with traceable references.
The exposition is original. No Active Calculus exercise is reproduced verbatim. Public-domain examples were modernized and recomposed when used as inspiration.
The verified handoff declares original composition and requires owner provenance review. BetterGrades-original material remains separate from public-domain references; no source textbook PDF is published here.