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Math Help - calculating limit of rational function

  1. #1
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    calculating limit of rational function

    I'm not sure what to do when I plug in "a" in a rational function if the numerator comes out as zero, here is the problem:

    lim (x+2)/(x^3+8)
    x--> -2

    the answer in the back is 1/12, could someone help me see how to find this?

    Thx!!!
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  2. #2
    Super Member Matt Westwood's Avatar
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    The thing is you got a fraction here:

    \frac {x+2} {x^3 + 8}

    where if you put x = -2 in, both the top and the bottom are zero.

    So what you do is you factorise the bottom, and you'll see that it has a factor of x+2. So divide top and bottom by x+2 and see what you're left with.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Matt Westwood View Post
    The thing is you got a fraction here:

    \frac {x+2} {x^3 + 8}

    where if you put x = -2 in, both the top and the bottom are zero.

    So what you do is you factorise the bottom, and you'll see that it has a factor of x+2. So divide top and bottom by x+2 and see what you're left with.
    to piggy back on this excellent advice, think "sum of two cubes"
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  4. #4
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    oh ok, I should have seen that, lol. thx!

    (x+2)/(x^2+4)(x+2) = 1/12 x--> -2
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by calcnewbie View Post
    oh ok, I should have seen that, lol. thx!

    (x+2)/[(x^2 - 2x +4)(x+2)] = 1/12 x--> -2
    see the correction above. somehow you got the right answer when you had the wrong factorization i don't see how, you must've mistyped
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