Let f be the function defined by f(x)=(x-4)/((x^2)-16).

By computing the values of f at 3.9,3.99,3.999 and 4.1,4.01,4.001 estimate the value of lim x->4 f(x).

3.9,3.99,3.999, 4.1,4.01,4.001
[10/79,100/799,1000/7999,10/81,100/801…

lim f(x) ~ 1/8
x->4

you can get it factoring the denominator
(x - 4)/(x^2 - 16) = (x - 4)/((x - 4)(x+4))
you cancel (x - 4) and get 1/(x+4)

lim 1/(x+4) = 1/(4+4) = 1/8
x->4