Let f be the function:(adsbygoogle = window.adsbygoogle || []).push({});

f(x) =

sin(x) ; x is element of Q

cos(x) ; x is not element of Q

Prove, using epsilon-delta definition, that there is a point c,which is element of R at which f is continuous.

Hint: Consider c such that sin(c) = cos(c); why does such a c exist? Then,

since you know that sin(x) and cos(x) are continuous at c, for epsilon> 0, you get delta1 >

0 that gives lsin(x)-sin(c)l <epsilon , and also delta2 > 0 that gives lcos(x)-cos(c)l <epsilon .

Now, why does delta = min(delta1; delta2) work to show lf(x)- f(c)l < epsilon.

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

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!

# Can anyone guide me for this question?

Loading...

Similar Threads - anyone guide question | Date |
---|---|

Need a quick favor if anyone has Differential Equations 3rd Ed by Zill | Oct 24, 2013 |

Workbook guide +problem in Math. Phys. | Sep 29, 2013 |

Can anyone help me? I have no idea . | Sep 14, 2013 |

Simple-looking 1st order DE, solution anyone? | Apr 15, 2013 |

Anyone have any ideas on a technique to tackle this pde | Jul 16, 2012 |

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