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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13.1 Finding Limits Numerically and Graphically

Focus on continuous limit and undefined point.

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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.

01Estimating limits numericallyWorked steps · five questions02One-sided limits and limits from a graphWorked steps · five questions
Lesson brief and rules

13.1 Finding Limits Numerically and Graphically

A limit describes what outputs approach near an input, even if the function is undefined there.

Worked example 11
01 / Find lim⁡x→4(3x+5)\displaystyle \lim x\to 4 (3x+5).
02 / A linear function is continuous; substitute 44 to get 1717.
03 / Answer: 1717
Worked example 2 · Undefined point

Can lim⁡x→4f(x)\displaystyle \lim x\to 4 f(x) exist if f(4)f(4) is undefined?

A limit concerns nearby values, not necessarily the value at the point. Answer: Yes

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One-sided limits and limits from a graph

A graph has a hole at (2,5)(2, 5) and f(2)=1f(2) = 1. lim⁡x→2f(x)\displaystyle \lim _{x\to 2} f(x)?
Graph for One-sided limits and limits from a graphThe graph corresponds to the stated function or supplied points.−4−224−2246xy
Solid: curve 1

55.

Answer: 55

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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