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Math Help - Infinite Limit

  1. #1
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    Question Infinite Limit

    Okay, so I'm having trouble with subbing in (-)infinity...
    a) lim x -> -inf. 1/x^3
    = 1/(-inf.)^3
    = 1/(-inf.)
    = -1/inf.
    = 0
    Right?
    Then consider this...:
    b) lim x-> -inf. -1/x^3
    = -1/(-inf.)^3
    = -1/(-inf.)
    = 1/inf. <--- 1) Do the (-)s cancel eachother out here?
    = 0
    Right?
    Now let's say this was part of a bigger eqn such that the eqn looked like:
    lim x-> -inf. of f(x)=(x^3)-1/(x^3)
    2) Would I have added the zero in my b example, taken it away,
    3) Or furthermore, would it be a 0- or 0+?
    4) Does it matter since it's a zero and therefore it wouldn't affect the result?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
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    Chicago, IL
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    Quote Originally Posted by krystaline86 View Post
    Okay, so I'm having trouble with subbing in (-)infinity...
    a) lim x -> -inf. 1/x^3
    = 1/(-inf.)^3
    = 1/(-inf.)
    = -1/inf.
    = 0
    Right?
    Then consider this...:
    b) lim x-> -inf. -1/x^3
    = -1/(-inf.)^3
    = -1/(-inf.)
    = 1/inf. <--- 1) Do the (-)s cancel eachother out here? I don't think it would really matter if it was negative or not. \frac{1}{\pm\infty}=0, whether if it was +\infty or -\infty.
    = 0
    Right?
    Now let's say this was part of a bigger eqn such that the eqn looked like:
    lim x-> -inf. of f(x)=(x^3)-1/(x^3)
    2) Would I have added the zero in my b example, taken it away,
    3) Or furthermore, would it be a 0- or 0+?
    4) Does it matter since it's a zero and therefore it wouldn't affect the result?
    In evaluating \lim_{x\to-\infty}x^3-\frac{1}{x^3}, we see that as x\to-\infty, x^3\to-\infty; and as x\to-\infty, -\frac{1}{x^3}\to 0, thus the limit would equal -\infty+0=\color{red}\boxed{-\infty}

    Does this clarify things?

    --Chris
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