Find the Taylor polynomial of degree 4 for $\cos(x)$, for $x$ near 0:
$P_{4}(x) =$

Approximate $\cos(x)$ with $P_{4}(x)$ to simplify the ratio:
${1 - \cos(x)\over x} =$

Using this, conclude the limit:
$\lim\limits_{x\to0}\,{1 - \cos(x)\over x} =$