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Math Help - Urgent Help! with Limits

  1. #1
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    Urgent Help! with Limits

    I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

    I need to find:
    the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
    and the lim as x goes to zero of the same function

    Please help!
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  2. #2
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    When taking the limit of a rational expression, if x approaches +/- infinity, you can disregard all but the coefficients of the highest powers.

    Therefore you have,

    \lim_{x\to\infty}\frac{3x^{2}}{4x^{2}}

    Now, you can see what it is?.

    As x approaches 0, look close, can you see it?.
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  3. #3
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    Quote Originally Posted by afn2

    I need to find:
    the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
    and the lim as x goes to zero of the same function
    Divide the numerator and denominator by x^2
    \lim_{x\to\infty}\frac{3+\frac{2}{x}+\frac{2}{x^2}  }{4+\frac{2}{x}+\frac{7}{x^2}}
    The numerator is,
    \lim_{x\to\infty} 3+\frac{2}{x}+\frac{2}{x^2}=3
    The denominaot is,
    \lim_{x\to\infty}4+\frac{2}{x}+\frac{7}{x^2}=4
    Since both limits exists thus the value of the limit is 3/4
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by afn2
    I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

    I need to find:
    the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
    and the lim as x goes to zero of the same function

    Please help!
    The limit as x goes to 0 should be simple. Both the numerator and denominator are continous functions on all real numbers (ie. the domain in both cases is all real numbers) and the denominator is not 0 for x = 0, so effectively all you need to do is substitute 0 for x in the expression.

    -Dan
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  5. #5
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    Thanks a bunch, I knew it was pretty simple, but I've always struggled with limits, even though I completely get derivatives and integrals. I just needed a push in the right direction. Thanks guys!
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