If `f(x)={(x-|x|)/x ,x!=0 2,x=0,s howt h a t("lim")_(xvec0)` `f(x)` does not exist.

Show that (lim)_(x rarr0)(x)/(|x|) does not exist.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

Let f(x)={{:((|x|)/(x)",",xne0),(2",",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(x) does not exist.

If f(x)=(|x|)/(x) , then show that lim_(xrarr0) f(x) does not exist.

Let f(x)={:{((3x)/(|x|+2x)',xne0),(0",",x=0.):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={x+5,quad if x>0x-4, if x<0 Prove that (lim)_(x rarr0)f(x) does not exist.

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

If f(x) is defined as follows: f(x){{:(1,x,gt0),(-1,x,lt0),(0,x,=0):} Then show that lim_(xrarr0) f(x) does not exist.

A function f(x) is defined as follows: f(x)=1 if x>0;-1 if x<0;0 if x=0. Prove that lim_(x rarr0)f(x) does not exist