Question

What is lim
x²-4?
X-2 X+2
O-4
O 0
04
ODNE

Answer 1

First answer choice

`- 4`

Explanation:

`\lim _(x\to \:-2)\left((x^2-4)/(x+2)\right)\\\\\\\mathrm{Simplify}\:(x^2-4)/(x+2)\\\\\\\mathrm{Factor}\:x^2-4:\quad (x + 2)(x - 2)\\\\\lim _(x\to \:-2)\left((x^2-4)/(x+2)\right) \\\\= \lim _(x\to \:-2)\left((x+2)(x-2))/(x+2)\right)`

The x+2 common factor cancels out

`= \lim _(x\to \:-2)\left(x-2\right)\\\\\text{Plug in the value x= -2}\\\\= -2 - 2\\= -4`

Answer 2

A

Explanation:

`\lim_(x \to -2) (x^(2)-4 )/(x+2) \\\lim_(x \to -2) ((x+2)(x-2))/(x+2)\\ \lim_(x \to -2) x-2\\= -4`