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Math Help - How is this a limit

  1. #1
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    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.
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  2. #2
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    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?)
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  3. #3
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    Re: How is this a limit

    Quote Originally Posted by skg94 View Post
    (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.
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