Let `f(x){{:((x)/(|x|)",",xne0),(0",",x=0):}` Show that `lim_(xrarr0)f(x)` does not exist.

Let `f(x){{:((x)/(|x|)",",xne0),(0",",x=0):}` Show that `lim_(xrarr0)f

1.	Let `f(x){{:((x)/(\|x\|)",",xne0),(0",",x=0):}` Show that `lim_(xrarr0)f(x)` does not exist.
Answer» `lim_(xto0^(+))f(x)=lim_(hto0)(0+h)=lim_(hto0)f(h)=lim_(hto0\|-h\|)=lim_(hto0)h/h=1" "[becausehgt0]` `lim_(xto0^(-))f(x)=lim_(hto0)f(0-h)=lim_(hto0)(-h)/(\|-h\|)=lim_(hto0)(-h)/(h)=-1.` `thereforelim_(xto0^(+))f(x)nelim_(xto0)f(x)and so limf(x)` does not exist.