calculus

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can someone please explain why the answer to this is negative infinity? I keep getting positive.

lim
x--> - infinity x^3-2/x^2+x

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  • calculus -

    Just get a feel for the numbers

    x ---> - infinity

    for very large negative numbers , x^3 - 2 becomes "
    "hugely negative"
    but x^2 + x becomes + "very large"
    since -/+ = - , and the numerator is larger than the denominator by a factor of x,
    the answer is -negative infinity

    or

    (x^3 - 2)/(x^2 + x) = x - 1 + (x+2)/(x^2+x)

    lim (x^3-2)/(x^2+x) as x---> -∞
    = lim (x-1) + lim (x+2)/(x^2+x) as x---> -∞

    since intuitively we can see that lim (x+2)/(x^2+x) --> 0 as x ---> -∞

    we are left with lim x-1 as x -->-∞
    which is -∞

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