<s>[INST] Limit of a rational function Calculate the limit
$$ \lim_{x \to 0} \frac{3x^{2} - \frac{x^{4}}{6}}{(4x^{2} - 8x^{3} + \frac{64x^{4}}{3} )}$$
I divided by the highest degree of x, which is $x^{4}$, further it gave 
$$ \frac{-\frac{1}{6}}{\frac{64}{3}} = \frac{-1}{128}$$ 
which is wrong... what is my error? 
 [/INST] At $0$ we have
$$x^4=o(x^2)\quad\text{and}\quad x^3=o(x^2)$$
so
$$ \lim_{x \to 0} \frac{3x^{2} - \frac{x^{4}}{6}}{(4x^{2} - 8x^{3} + \frac{64x^{4}}{3} )}=\lim_{x \to 0}\frac{3x^2}{4x^2}=\frac34$$
</s>