EXAMPLE 8 Prove that the limit does not exist.\

\\\\lim_(x->2)(|x-2|)/(x-2)

\ SOLUTION\

\\\\lim_(x->2^(+))(|x-2|)/(x-2)=\\\\lim_(x->2^(+))(x-2)/(x-2)=\ \\\\lim_(x->2^(-))(|x-2|)/(x-2)=\\\\lim_(x->2^(-))(2-x)/(x-2)=

\ Since the right- and left-hand limits are different, it follows from this the the function

f(x)=|x-2(|

|)/(

x-2)

| to the left supports the one-sided

|

|

EXAMPLE 8 Prove that the limit does not exist. limx2x2x2 SOLUTION limx2+x2x2=limx2+x2x2=limx2x2x2=limx2x22x= Since the right- and left-hand limits are different, it follows from this the the function f(x)=x2/(x2) to the left supports the one-sided li