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

`image`

Answer 2

The limit is -4

Step-by-step explanation

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

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

`\displaystyle\lim_(x\to -2) ((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`