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Math Help - evaluating limits

  1. #1
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    evaluating limits

    Hi all,

    I need some help evaluating the following limit:

    lim x-->-3 pi/(x+3)^3

    I believe that the limit does not exist but i don't know how to explain it.

    Thanks in advance,
    ArTiCk
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I need some help evaluating the following limit:

    lim x-->-3 pi/(x+3)^3

    I believe that the limit does not exist but i don't know how to explain it.

    Thanks in advance,
    ArTiCk
    The limit is of the form
    \frac{\pi}{0}

    Any limit of the form (something other than 0)/0 does not exist as the operation is undefined. Only when you have 0/0 is it possible to have a solution (but it won't always.)

    -Dan
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  3. #3
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I need some help evaluating the following limit:

    lim x-->-3 pi/(x+3)^3

    I believe that the limit does not exist but i don't know how to explain it.

    Thanks in advance,
    ArTiCk
    Quote Originally Posted by topsquark View Post
    The limit is of the form
    \frac{\pi}{0}

    Any limit of the form (something other than 0)/0 does not exist as the operation is undefined. Only when you have 0/0 is it possible to have a solution (but it won't always.)

    -Dan
    Topsquark, this is a very rare (the only, so far?) occassion when I will disagree with you .....

    The limit does not exist because the left hand limit is not equal to the right hand limit:

    \lim_{x \rightarrow -3^+} \frac{\pi}{(x+3)^3} = + \infty.

    \lim_{x \rightarrow -3^-} \frac{\pi}{(x+3)^3} = - \infty.

    Technically \lim_{x \rightarrow -3} \frac{\pi}{(x+3)^{\color{red}2}} does exist: ~ \lim_{x \rightarrow -3} \frac{\pi}{(x+3)^2} = + \infty ......

    Where's referee TPH ....?
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