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Thread: Determining limits

  1. #1
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    Determining limits

    I have to determine the limits from the following expressions:

    Determining limits-limit.png

    I have the results available but I have no idea what to do, how to do it and why I have to do.
    I have searched theses forums and the internet as well as my syllabus for an explanation but have been unable to find one so hope people can help out.
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  2. #2
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    Re: Determining limits

    For this type of problem with rational functions of polynomials, we divide numerator and denominator by the greatest power of $n$ in the expression. This makes those terms tend to a constant while the rest go to zero.

    The second example:
    \begin{align*} \lim_{n \to \infty} \frac{3n^2 - 4}{-2n^3 +7} &= \lim_{n \to \infty} \frac{\frac{1}{n^3}(3n^2 - 4)}{\frac{1}{n^3}(-2n^3 +7)} \\ &=  \lim_{n \to \infty} \frac{\frac3n - \frac4{n^3}}{-2 +\frac7{n^3}} \\ &= \frac{0+0}{-2+0} \\ &= 0 \end{align*}
    Thanks from completelylost
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  3. #3
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    Re: Determining limits

    Thanks I get it now
    Thanks from Archie
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  4. #4
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    Re: Determining limits

    Once you have done that a few times, you should be able to see that:

    \lim_{x\to \infty}\frac{a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0}{b_mx^m+ b_{m-1}x^{m-1}+ \cdot\cdot<br />
\cdot+ b_1x+ b_0} is

    1) \infty if n> m.

    2) 0 if n< m.

    3) \frac{a_n}{b_m} if m= n
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