hello all,(adsbygoogle = window.adsbygoogle || []).push({});

i have been working on problems with continuity and i have come across some question in which i understand generally what i have to do but i just dont know where to start and how to put it together

a function f:R->R is said to be periodic if there exists a number k>0 such that

f(x+k)=f(x) for all x an element of R. suppose that f:R->R is continuous and periodic. Prove that f is bounded and uniformly continuous on R.

also

let f:R-->R be a function which satisfies the conditions

f(x+y)=F(x)+f(y)

and

f(-x)=-f(x) for al x znd y an element of R

suppose that f is continuous at 0 show that f is continuous at every point in R

please help

Steven

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Problems with continuity

Loading...

Similar Threads - Problems continuity | Date |
---|---|

Continuity Problem | Mar 31, 2011 |

Continuity homework problem | Apr 12, 2010 |

Continuity problem | Sep 5, 2009 |

A Problem About Uniformly Continuous functions | Sep 20, 2008 |

Problems relating to Absolute Continuity | Aug 15, 2007 |

**Physics Forums - The Fusion of Science and Community**