Question

Find the limit of the function algebraically. limit as x approaches negative 2 of quantity x squared minus four divided by quantity x plus 2.

Answer 1

$\displaystyle \lim_{x\to -2}\dfrac{x^2-4}{x+2}= \lim_{x\to -2}\dfrac{(x-2)(x+2)}{x+2}= \lim_{x\to -2}(x-2)=-2-2=-4$

Answer 2

ANSWER

The limit is -4

EXPLANATION

   $\displaystyle\lim_{x\to -2} \dfrac{x^2-4}{x+2}$

The numerator factors into (x-2)(x+2)

   $\displaystyle\lim_{x\to -2} \dfrac{(x-2)(x+2)}{x+2}$

The (x+2) cancel out

   $\displaystyle\lim_{x\to -2} (x-2)$

By direct substitution

   $\displaystyle\lim_{x\to -2} (x-2) = -2 -2 = -4$