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Worked problem · Calculus I · Unit 1

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

Problem

  1. Evaluate lim⁡x→3x2−9x−3\lim_{x\to3}\frac{x^2-9}{x-3}.

Complete worked solutions

Every problem has a source-matched answer and independently reviewed derivation.

01

Problem 1: Evaluate lim⁡x→3x2−9x−3\lim_{x\to3}\frac{x^2-9}{x-3}.

Answer: 66

Why this method: Factoring and cancellation matches the mathematical structure before any algebraic cleanup.

  1. Factor the vanishing numerator as (x−3)(x+3)(x-3)(x+3).
  2. Cancel the common factor only for nearby inputs, then substitute the target.
  3. The simplified expression approaches 66.

What is included

See a concise answer and full derivation for evaluate limit as x approaches 3 x squared minus 9 over x minus 3.

Skills assessed

  • Factoring and cancellation

Prerequisites

  • function notation
  • algebraic factoring

Common errors

  • Cancelling terms that are added instead of common factors.

Learn fully

Supporting steps