Calculus I · Limits and Continuity · quiz

Epsilon-Delta Concept Quiz

Test Epsilon-Delta Concept Quiz with short answer checks, hints, worked feedback, and links back to the exact lessons you need.

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Chapter 6 Concept Quiz

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

Interactive checkepsilon-linear-q1

For $f(x)=3x+1$ at $x=2$ , give a working choice of $\delta$ in terms of $\varepsilon$ .

Your work stays on this device. No account or AI grader is used.

Show hint

$|f(x)-7|=3|x-2|$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkepsilon-linear-q2

For $f(x)=5x$ at $x=1$ , give a working $\delta$ .

Your work stays on this device. No account or AI grader is used.

Show hint

$|5x-5|=5|x-1|$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkepsilon-quadratic-q1

For the standard proof that $x^2\to4$ as $x\to2$ , enter the usual safe choice of $\delta$ .

Your work stays on this device. No account or AI grader is used.

Show hint

First require $|x-2|<1$ , which makes $|x+2|<5$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkformal-reading-q1

In $|f(x)-L|<\varepsilon$ , does $\varepsilon$ control input distance or output distance?

Your work stays on this device. No account or AI grader is used.

Show hint

Look at which quantities are being compared.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

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.

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.

Chapter 6 Concept Quiz

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

Interactive checkepsilon-linear-q1

For $f(x)=3x+1$ at $x=2$ , give a working choice of $\delta$ in terms of $\varepsilon$ .

Your work stays on this device. No account or AI grader is used.

Show hint

$|f(x)-7|=3|x-2|$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkepsilon-linear-q2

For $f(x)=5x$ at $x=1$ , give a working $\delta$ .

Your work stays on this device. No account or AI grader is used.

Show hint

$|5x-5|=5|x-1|$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkepsilon-quadratic-q1

For the standard proof that $x^2\to4$ as $x\to2$ , enter the usual safe choice of $\delta$ .

Your work stays on this device. No account or AI grader is used.

Show hint

First require $|x-2|<1$ , which makes $|x+2|<5$ .

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Interactive checkformal-reading-q1

In $|f(x)-L|<\varepsilon$ , does $\varepsilon$ control input distance or output distance?

Your work stays on this device. No account or AI grader is used.

Show hint

Look at which quantities are being compared.

Attempt once to unlock the solution

Submit an answer first. The hint is available now.

Summary

Quiz use on the website

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.

Chapter 6 Concept Quiz

Related resources

Original instruction with traceable references.

Chapter 6 Concept Quiz

Related resources

Original instruction with traceable references.