<s>[INST] Prove using the formal definition of a limit that How would I go about proving this limit?
$\lim_{x\to\infty}\frac{1}{x^4+x^2+5}=0$
so far I have:
$|f(x) -L|< ϵ$ wherever $x > N$
$|\frac{1}{x^4+x^2+5} - 0| < ϵ $ wherever $x > N$
$|\frac{1}{x^4+x^2+5}| < ϵ  ,\; x > ∞$, assuming, $x > 0$
taking the absolute value $\frac{1}{x^4+x^2+5} < ϵ$
${x^4+x^2+5}$ > $\frac{1}{ϵ}$
i am not sure whether this is correct, but what would be the next step?
 [/INST] HINT:
$$\frac{1}{x^4+x^2+5}\le \frac{1}{x^4}<\epsilon$$
whenever $x>B=\epsilon^{-1/4}$.
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