Approximated by a parabola

    Notice that    is an even function. The following computation shows that the first term in the Maclaurin series is .  For this reason it is often claimed that the shape of a hanging cable is "approximated by a parabola."  

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Exploration 2.

Find the Maclaurin series for  .

The general term in the series is  .  Summing the first six terms in the series, we get   

Mathematica is able to sum the infinite series.  

(c) John H. Mathews 2004