Concept preview

What you will be able to do

1. 01Read the same limit from four representations — graph, table, algebraic formula, and verbal/contextual description — and see that they agree.
2. 02Translate a limit stated in one representation into any of the others, and match graphs, tables, and formulas that describe the same limit.
3. 03Use cross-representation checking to catch errors and to choose the most efficient method for a given problem.

Take one concrete limit and turn it over in your hands: $\lim_{x\to2}\frac{x^2-4}{x-2}.$ Over the next few paragraphs we will read this exact limit as a graph, as a table, as an algebraic simplification, and as a verbal statement about a rate — and every route will land on the same number, $4$. When four independent methods agree, you can trust the answer completely; when they disagree, one of them has exposed a mistake worth finding.