Question

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

Answer 1

=`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