MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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13.2 Finding Limits Algebraically

Focus on removable factor and direct substitution.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Limit laws and direct substitutionWorked steps · five questions02Limits by factoring and rationalizingWorked steps · five questions
Lesson brief and rules

13.2 Finding Limits Algebraically

Factor and cancel only for x≠x\ne a, then evaluate the simplified expression as xx approaches aa.

Worked example 11
01 / Find lim⁡x→4x2−16x−4\displaystyle \lim x\to 4 \dfrac{x^{2}-16}{x-4}.
02 / For x≠4x\ne 4, cancel x−4x-4: expression is x+4x+4. Its limit is 88.
03 / Answer: 88
Worked example 2 · Direct substitution

Find lim⁡x→4(6x+1)\displaystyle \lim x\to 4 (6x+1).

A polynomial is continuous; substitute x=4x=4. Answer: 2525

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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