Question

Find the limit of the function algebraically. (1 point)limit as x approaches negative four of quantity x squared minus sixteen divided by quantity x plus four

Answer 1

We are asked to find the limit of the following function.

$\lim_{n\to-4}\;\frac{x^2-16}{x+4}$

As you can see, we cannot directly plug the value x = -4 into the function because it will make the denominator 0 and the function will be undefined.

First, we have to factor out the numerator.

$x^2-16\Rightarrow x^2-4^2\Rightarrow(x+4)(x-4)$

So, the function becomes

$\lim_{n\to-4}\;\frac{x^2-16}{x+4}\Rightarrow\frac{(x+4)(x-4)}{(x+4)}\Rightarrow(x-4)$

Finally, now we can plug the limit x = -4 into the above function

$\lim_{n\to-4}\;(x-4)\Rightarrow(-4-4)\Rightarrow-8$

Therefore, the limit of the given function is equal to -8