Uniform continuity

Uniform continuity

Assessment

Flashcard

Mathematics

University

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is uniform continuity?

Back

A function f is uniformly continuous on a set X if for every ε > 0, there exists a δ > 0 such that for all x, y in X, if |x - y| < δ, then |f(x) - f(y)| < ε.

2.

FLASHCARD QUESTION

Front

Are linear functions uniformly continuous on all of ℝ?

Back

Yes, linear functions are uniformly continuous on all of ℝ.

3.

FLASHCARD QUESTION

Front

Are quadratic functions uniformly continuous on all of ℝ?

Back

No, quadratic functions are not uniformly continuous on all of ℝ; they are only uniformly continuous on closed intervals.

4.

FLASHCARD QUESTION

Front

What does it mean for a function to be continuous?

Back

A function f is continuous at a point c if for every ε > 0, there exists a δ > 0 such that if |x - c| < δ, then |f(x) - f(c)| < ε.

5.

FLASHCARD QUESTION

Front

What is the relationship between uniform continuity and continuity?

Back

Uniform continuity implies continuity, but continuity does not imply uniform continuity.

6.

FLASHCARD QUESTION

Front

What is the continuous image of a compact set?

Back

The continuous image of a compact set is compact.

7.

FLASHCARD QUESTION

Front

What is the continuous image of a connected set?

Back

The continuous image of a connected set is connected.

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