Question

Given `k(x) = (x^3 - 2x - 4)/(x-2)` how do you find the limit as x approaches 2?

Answer 1

Factor, reduce and evaluate.

Explanation:

`lim_(xrarr2) (x^3-2x-4)/(x-2)` has indeterminate initial form `0/0`.

Since `2` is a zero of the polynomial `x^3-2x-4`, we can be certain that `x-2` is a factor.

Use division (long or synthetic) or step-by-step reasoning to find

`x^3-2x-4 = (x-2)(x^2+2x+2)`

`lim_(xrarr2) (x^3-2x-4)/(x-2) = lim_(xrarr2) ((x-2)(x^2+2x+2))/(x-2)`

`= lim_(xrarr2) (x^2+2x+2)`

`= 4+4+2 = 10`