Extension: Uniform Continuity
Read this topicExplanations 2
- Continuity at a point (which you may or may not have seen yet) is defined as follows: A function fff is continuous at a point ppp if for every ϵ>0\epsilon > 0ϵ>0, there exists a…
By Evan Chen, Victor Wang, Expii Team, Alex Federspiel, Moor Xu
- (Video) Continuous and Uniformly Continuous Functions by Steve Stein Here's a video by Steve Stein explaining what uniform continuity is and how it differs from regular continuity.
By Alex Federspiel
Problems 7
- True or False\text{True or False}True or False === Every function that is uniformly continuous is also continuous.
- True or False\text{True or False}True or False === f(x)=xf(x)=\sqrt{x}f(x)=x is uniformly continuous on [0,∞)[0,\infty)[0,∞).
- True or False\text{True or False}True or False === f(x)=x3f(x)=x^3f(x)=x3 is uniformly continuous on R\mathbb{R}R.
- True or False\text{True or False}True or False === f(x)=sin(1x)f(x)=\sin(\frac1x)f(x)=sin(x1) is uniformly continuous on (0,1](0,1](0,1].
- True or False\text{True or False}True or False === f(x)=x2f(x)=x^2f(x)=x2 is uniformly continuous on [0,1][0,1][0,1].
- True or False\text{True or False}True or False === f(x)=x2f(x)=x^2f(x)=x2 is uniformly continuous on R\mathbb{R}R.
- True or False\text{True or False}True or False === If f(x)f(x)f(x) is continuous on [a,b][a,b][a,b], then f(x)f(x)f(x) is uniformly continuous on [a,b][a,b][a,b].