onstruct a function f:R$$Rf: $\backslash$mathbb$\{$R$\}\backslash$to $\backslash$mathbb$\{$R$\}$f:R$$R such that:

limx$0$f$($x$)\backslash$lim$\_\{$x $\backslash$to $0\}$ f$($x$)$limx$0$f$($x$)$ exists, and

For every x$0$x

e $0$x$=0,$ the limit limx$$xf$($x$)\backslash$lim$\_\{$x $\backslash$to x$\}$ f$($x$)$limx$$x$$f$($x$)$ does not exist.