Epsilon Delta Proofs Quizzes, Questions & Answers

Top Trending Epsilon Delta Proofs Quizzes

Ready to apply ε–δ reasoning to a variety of functions? This quiz gives you hands-on practice with the limit definition using deleted neighborhoods, bounding techniques, rational functions, absolute values,...

Questions: 15 | Attempts: 29 | Last updated: Jan 27, 2026

Sample Question 1
Which statements correctly express the ε–δ definition of limit?

For every ε > 0, there exists δ > 0

If 0 < |x − a| < δ, then |f(x) − L| < ε

F(a) must equal L for the limit to exist

δ depends on ε

Sample Question 2
Which of the following must be true for f to be continuous at a?

F(a) exists

Limₓ→ₐ f(x) exists

Limₓ→ₐ f(x) = f(a)

The function is differentiable at a

Sample Question 3
In the ε–δ definition, ε represents:

Output closeness

Input closeness

A positive number

A distance between x and a

Recent Epsilon Delta Proofs Quizzes

Foundations of Epsilonâ€“Delta Proofs Quiz

Think you understand the ε–δ definition of limits and continuity? This quiz helps you apply the formal framework behind limits, piecewise continuity, and δ-selection strategies. You’ll work through...

Questions: 15 | Attempts: 13 | Last updated: Jan 27, 2026

Sample Question
If |x−a| < δ implies |f(x)−L| < ε, then the limit exists and equals L.

True

False

Epsilonâ€“Delta Continuity Quiz

Ready to practice the formal definition of continuity? This quiz helps you understand how ε–δ arguments connect input closeness to output closeness. You'll test your knowledge of when functions satisfy the...

Questions: 15 | Attempts: 12 | Last updated: Jan 27, 2026

Sample Question
If a function is continuous at a, then for every ɛ>0, there exists a δ>0 such that whenever |x−a|<δ, we have |f(x)−f(a)|<ɛ.

True

False