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)\;(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)\;(x^2-16)/(x+4)\Rightarrow((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