Limit By Factoring: Worked Example and Solution
A complete factoring and cancellation example with method choice, derivation, verification, and a common wrong approach.
1 problem8 min estimated timeFoundational to intermediate progression
What is included
See a concise answer and full derivation for evaluate \(\lim_{x\to3}\frac{x^2-9}{x-3}\).
Skills assessed
- Factoring and cancellation
Prerequisites
- function notation
- algebraic factoring
Printable preview
- Evaluate .
Complete worked solutions
Every problem has a source-matched answer and independently reviewed derivation.
01
Problem 1: Evaluate .
Answer:
Why this method: Factoring and cancellation matches the mathematical structure before any algebraic cleanup.
- Factor the vanishing numerator as .
- Cancel the common factor only for nearby inputs, then substitute the target.
- The simplified expression approaches .
Common errors
- Cancelling terms that are added instead of common factors.