# How do you show the limit does not exist #lim_(x->4)(x-4)/(x^2-8x+16)# ?

##### 1 Answer

Aug 4, 2014

=

#oo#

Solution

#=lim_(x→4)((x-4)/(x^2-8x+16))# , plugging the limit we get#0/0#

#=lim_(x→4)((x-4)/(x^2-4x-4x+16))#

#=lim_(x→4)((x-4)/(x(x-4)-4(x-4)))#

#=lim_(x→4)(x-4)/((x-4)^2)#

#=lim_(x→4)1/((x-4))# Now applying the limit, we get

#=1/0=oo# , which implies limit does not exist