Limits: getting close to a number
Fill in a table of values close to a point where a function is undefined, read the limit from the graph, and see why the left-hand and right-hand limits must agree.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- France: grade 12
- Germany: grade 11
- Iran: grade 11
- Afghanistan: grade 12
- Syria: grade 11
- Palestine: grade 11
- Russia: grade 10
Guide
A limit asks: as x gets close to a number (without reaching it), which number does f(x) get close to? It is not the same as the value of the function at that point; the function may not even be defined there.
You can approach from two sides: from the left (the left-hand limit) and from the right (the right-hand limit). If both reach the same number, that number is the limit. If they differ, the limit does not exist.