Calculus I · Limits and Continuity · quiz

Finite Limits Concept Quiz

Section 2 Concept Quiz

Use this as a short retrieval check after finishing the section. On the website, each item should accept an answer before revealing the hint and worked explanation.

Interactive checksubstitution-q1

Evaluate $\lim_{x\to3}(2x+5)$ .

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This linear function is continuous, so substitute $x=3$ .

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Interactive checkfactor-q1

Evaluate $\lim_{x\to4}\frac{x^2-16}{x-4}$ .

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Factor $x^2-16=(x-4)(x+4)$ .

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Interactive checkradical-q1

Evaluate $\lim_{x\to0}\frac{\sqrt{x+9}-3}{x}$ .

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Multiply by the conjugate $\sqrt{x+9}+3$ .

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Interactive checkabs-q1

Does $\lim_{x\to0}|x|/x$ exist? Enter DNE if it does not.

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Check the left and right sides separately.

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Summary

Quiz use on the website

This page should report completion by concept, not merely a total score. A wrong answer should link back to the exact lesson that teaches the missing method. The same questions may appear in randomized numerical variants, but the canonical explanation should remain stable.

After the explanation

Use the section idea

Reading lens

What did direct substitution reveal, and which algebraic move removes the obstacle without changing nearby behavior?

Mental model

Substitution is a diagnostic first move: a real number usually finishes the problem, while an indeterminate form asks for a structural rewrite.

Decision

Match the obstacle to the algebra—factor polynomial zeros, rationalize radicals, combine complex fractions, and split absolute values into one-sided cases.

Common trap

Zero over zero is not an answer, and cancellation is legal only for factors after the expression has been rewritten as a product.

Check yourself

You are ready to move on when you can justify why each rewrite preserves nearby values even if the original expression is undefined at the target.

Source & rights

Original instruction with traceable references.

The exposition is original. No Active Calculus exercise is reproduced verbatim. Public-domain examples were modernized and recomposed when used as inspiration.

The verified handoff declares original composition and requires owner provenance review. BetterGrades-original material remains separate from public-domain references; no source textbook PDF is published here.