Find \(\lim_{(x,y) \to (0,0)} f(x,y)\), where \[ f(x,y) = \begin{cases} x + y \sin\frac{1}{x}, & x \neq 0, \\ 0, & x = 0. \end{cases} \] Do the limits \(\lim_{x \to 0}\left(\lim_{y \to 0} f(x,y)\right)\) and \(\lim_{y \to 0}\left(\lim_{x \to 0} f(x,y)\right)\) exist?
Double and iterated limits of $x+y\sin\frac1x$
P-TRIV-RA14
- Area
- Real Analysis
- Status
- draft