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November 13th, 2017, 08:03 AM   #1
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Math Focus: dynamical systen theory
Concerning infinity as a limit

Dear MyMathForum Community:
This is the problem:

as x --> infinity, (2x+3)/(5x+7) = 2/5. Why is this so? Thank you.
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November 13th, 2017, 08:22 AM   #2
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\begin{align*}\frac {2x+3}{5x+7}&= \frac{\frac25(5x+7)+\frac15}{5x+7} \\ &= \frac25 \cdot \frac{5x+7}{5x+7} +\frac15 \cdot \frac1{5x+7} \\
&= \frac25 +\frac1{5(5x+7)} \end{align*}

An easier way to get the same result is $$\frac {2x+3}{5x+7} = \frac{2 + \frac3{x}}{5+\frac7{x}}$$

Last edited by v8archie; November 13th, 2017 at 08:28 AM.
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