# Thread: How is this a limit

1. ## How is this a limit

(x^2+16x+64)/(x+8)

So i factored and simplified to (x+8) from the left its negative infinity and the right positive infinity right? My textbook says its a limit with a value of 0 (lim x --> -8)

Also

lim x--> 3 = 1 / (x-3)^2 from both the left and right would be positive infinity if i understand limits right. My textbook says its not a limit.

2. ## Re: How is this a limit

Hey skg94.

For the second one, something is a limit if the limit exists from both sides with the same value. I think this should be a limit as well (does your question ask about 1/(x-3) instead?)

3. ## Re: How is this a limit

Originally Posted by skg94
(x^2+16x+64)/(x+8)

So i factored and simplified to (x+8) from the left its negative infinity and the right positive infinity right? My textbook says its a limit with a value of 0 (lim x --> -8)

Also

lim x--> 3 = 1 / (x-3)^2 from both the left and right would be positive infinity if i understand limits right. My textbook says its not a limit.
For the first one, the function \displaystyle \begin{align*} \frac{x^2 + 16x + 64}{x + 8} \end{align*} is identical to \displaystyle \begin{align*} x + 8 \end{align*} everywhere except where \displaystyle \begin{align*} x = -8 \end{align*} because the function would be undefined. But the function will still approach the same value as it would in the function \displaystyle \begin{align*} x + 8 \end{align*}, because they are identical everywhere else.