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Math Help - Limits

  1. #1
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    Limits

    lim 1/x + 3 = 3 right?
    x -> ∞

    what about

    lim
    x -> ∞ 3x + 2/4x?

    and

    lim 5x - 8/7x^2 - 14?
    x -> ∞
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  2. #2
    Super Member Random Variable's Avatar
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    Do you mean  \lim_{x \to \infty} \frac{3x +2}{4x} ?

    =  \lim_{x \to \infty} \frac{\frac{3x}{x} + \frac{2}{x}}{\frac{4x}{x}} = \lim_{x \to \infty} \frac{3+\frac{2}{x}}{4}= \frac{3+0}{4} =\frac{3}{4}
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  3. #3
    MHF Contributor Calculus26's Avatar
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    For limits at infinity consider the ratio of the highest powered terms

    lim(3x+2)/(4x) = lim 3x/4x = 3/4

    lim(5x-8)/(7x^2-14) = lim 5x/7x^2 = lim 5/(7x) = 0
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