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

Show that Lim_(x to 0 ) 1/x does not exist .

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

Show that Lim_(x to 0 ) e^(-1//x) does not exist .

Show that Lim_(x to 0 ) sin (1/x) does not exist .

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) , then show that lim_(xrarr0) f(x) does not exist.

Show that Lim_( xto 2) (|x-2|)/(x-2) does not exist .

Show that Lim_(x to 0 ) (| sin x |)/x does not exist .