Calculus I · Limits and Continuity · quiz

Limit Meaning Concept Quiz

Section 1 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 checklimit-meaning-q1

If $\lim_{x\to 4}f(x)=7$ , what output value is approached?

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The number after the equals sign is the output target.

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Interactive checkone-sided-q1

A graph approaches $3$ from the left at $x=2$ . What is $\lim_{x\to2^-}f(x)$ ?

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The superscript minus means use inputs smaller than $2$ .

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Interactive checkhole-q1

A curve approaches the open point $(1,5)$ , while a filled point is at $(1,9)$ . What is the limit as $x\to1$ ?

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The limit follows the nearby curve, not the filled point.

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Interactive checkrate-q1

An average-rate expression simplifies to $12-2h$ . What value does it approach as $h\to0$ ?

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Set only the limiting value of $h$ after simplification.

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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 are nearby outputs doing as the input approaches the target from both sides?

Mental model

Imagine tightening a window around the target input and watching where all nearby outputs are forced to gather.

Decision

Read the left-hand and right-hand behavior separately first; combine them only after both sides approach the same output.

Common trap

The function value at the target can be missing or deliberately moved, so never substitute a plotted dot for evidence from both sides.

Check yourself

You understand the section when you can explain a limit from a graph, table, and sentence without confusing it with the function value.

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.