If `f(x)=(|x|)/(x)`, then show that `underset(xrarr0)"lim"f(x)` does not exist.

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

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

If f(x)={(x-|x|)/x ,x!=0, 2,x=0 , show that lim_(xrarr0) f(x) does not exist.

Show that lim_(xrarr2) ([x-2])/(x-2) does not exist.

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.

Show that ("lim")_(x->0)\ e^(-1//x) does not exist.

Given f(x)={((x+|x|)/x,x!=0),(-2,x=0):} show that lim_(xto0)f(x) does not exist.

underset(xrarr0)(lim)(sinnx)/x is equal to

Let f(x) be a function defined by f(x) = {{:((3x)/(|x|+2x),x ne 0),(0,x = 0):} Show that lim_(x rarr 0) f(x) does not exist.

Show that ("lim")_(x->0)x/(|x|) does not exist.