Question

How do you find the limit of `(x^3 - 27) / (x^2 - 9)` as x approaches 3?

Answer 1

`L_(x->3)(x^3-27)/(x^2-9)=9/2`

Explanation:

`L_(x->3)(x^3-27)/(x^2-9)`

= `L_(x->3)((x-3)(x^2+3x+9))/((x-3)(x+3)`

= `L_(x->3)(cancel((x-3))(x^2+3x+9))/(cancel((x-3))(x+3)`

= `L_(x->3)(x^2+3x+9)/(x+3)`

= `L_(x->3)(3^2+3xx3+9)/(3+3)`

= `L_(x->3)(9+9+9)/6=27/6=9/2`