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.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) 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.

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

Given f(x)={((x+|x|)/x,x!=0),(-2,x=0):} show that lim_(xto0)f(x) 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.

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.

Find lim_(xrarr0) f(x) where f(x)={{:((x)/(|x|),xne0),(0,x=0):}

If f(x)={(3x+2,"when "x ne0),(0,"when "x =0):}} , what does lim_(x to 0)f(x) equal ?