2
$\begingroup$

$f(x,y) =\begin{cases}\arctan(y/x) & x\neq 0\\ \pi/2 & x=0,y>0\\-\pi/2 & x=0,y<0.\end{cases}$

$f$ is defined on $\Bbb R^2\smallsetminus\{(0,0)\}.$

Show that $f$ is continuously differentiable on all of its domain.

Also use implicit function to show the above proof again.

Thanks!

  • 1
    You're repeating *exactly* your question from 3 hours ago. You must be patient and wait until somebody deals with that, and not send over and over the same question.2012-10-28
  • 1
    I have no idea what your inequalities and bounds for $x$ and $y$ represent. Please fix those yourself.2012-11-01
  • 0
    So...are you dividing by $0$ in there? That's...bad.2012-11-01
  • 0
    that's a function with different values in different domains2012-11-01
  • 0
    Ah, I see. Please tell me if my interpretation is right.2012-11-01

1 Answers 1