<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] $$ \lim_{x \to 0} \frac{3x^{2} - \dfrac{x^{4}}{6}}{(4x^{2} - 8x^{3} + \dfrac{64x^4}{3} )}$$
$$=\lim_{x\to0}\frac{x^2\left(3-\dfrac{x^2}6\right)}{x^2\left(4-8x+\dfrac{64}3x^2\right)}$$
Cancel out $x^2$ as $x\ne0$ as $x\to0$
Then set $x=0$ as it is no longer of the form $\dfrac00$
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