Hi(adsbygoogle = window.adsbygoogle || []).push({});

If the function ##f(x,y)## is independently continuous in ##x## and ##y##, i.e.

[itex]f(x+d_x,y) = f(x,y) + \Delta_xd_x + O(d_x^2)[/itex] and [itex]f(x,y+d_y) = f(x,y) + \Delta_yd_y + O(d_y^2)[/itex]

for some finite ##\Delta_x##, ##\Delta_y##, and small ##\delta_x##, ##\delta_x##,

does it mean that it is continuous in both?

[itex]f(x+d_x,y+d_y) = f(x,y) + \Delta_xd_x +\Delta_yd_y+O(d_x^2,d_y^2)[/itex]

How about differentiability? (if the function is independently differentiable in ##x## and ##y##, is it differentiable in both ##x## and ##y##?)

Cheers

wavingerwin

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Continuity and differentiability in two variables

Tags:

Loading...

Similar Threads for Continuity differentiability variables |
---|

B When do we use which notation for Delta and Differentiation? |

I Video (analytic continuation) seems to mix 4-D & 2-D maps |

B Product rule OR Partial differentiation |

A Differential operator, inverse thereof |

A Continuous mass distribution |

**Physics Forums | Science Articles, Homework Help, Discussion**