evaluate each limit, if it exists
Lim as x approaches -2
(x^4 - 16) / (x+2)
You can factor out the x+2.
x^4 - 16 = (x^2+4)(x^2-4)
= (x^2+4)(x-2)(x+2)
So the ratio is always
(x^2+4)(x-2)
Evaluate that at x=-2
To evaluate the limit of (x^4 - 16) / (x + 2) as x approaches -2, we can substitute -2 into the expression and see if it yields a valid value.
Let's plug in x = -2:
((-2)^4 - 16) / (-2 + 2)
= (16 - 16) / 0
At this point, we can see that the denominator is equal to 0. When the denominator is 0, the expression becomes undefined, meaning the limit does not exist.
Therefore, the limit of (x^4 - 16) / (x + 2) as x approaches -2 does not exist.