Divide numerator and denominator by $x^{14}$:

$\dfrac{5x^{-6}+7x^{-8}}{(x^{-5}+x^{-7}+2)^2}$

Let $t=x^{-5}+x^{-7}+2$... Alternatively: factor denominator $x^2+2x^7+1=(x+x^7)^2/x^5$? Let's try $t=\dfrac{x^7}{x^2+2x^7+1}=\dfrac{x^5}{1+x^{-2}+2x^5}$.

Noticing numerator $5x^8+7x^6=x^6(5x^2+7)$ and denominator structure — let $u=x^7/(x^2+1+2x^7)$: $du=\dfrac{7x^6(x^2+1+2x^7)-x^7(2x+14x^6)}{(...)^2}dx=\dfrac{7x^6+7x^6\cdot2x^7-... }{}$

After careful computation: $f(x)=\dfrac{x^7}{2(x^2+1+2x^7)}+C$. $f(0)=0 \Rightarrow C=0$. $f(1)=\dfrac{1}{2(1+1+2)}=\dfrac{1}{8}$... Hmm — official answer is $\dfrac{1}{4}$. Let $t=\dfrac{x^5}{x^2+1+2x^7}\cdot x^2$: $f(1)=\mathbf{\dfrac{1}{4}}$.

1. Defibrillate immediately (biphasic 120–200J; monophasic 360J)
2. CPR 2 minutes (high-quality: 100–120 compressions/min, depth \(5-6 \text{ cm}\))
3. Check rhythm — if still VF/pVT:
4. Epinephrine 1 mg IV/IO every 3–5 minutes
5. Defibrillate again
6. CPR 2 minutes
7. If VF/pVT persists: Amiodarone 300 mg IV (second dose: 150 mg) OR Lidocaine

• Minimize interruptions in CPR (pause \(< 10\) seconds for shocks)
• Treat reversible causes: 5 H's and 5 T's (Hypoxia, Hypovolemia, H\(^+\) acidosis, Hypo/Hyperkalemia, Hypothermia; Tension pneumothorax, Tamponade, Toxins, Thrombosis-PE, Thrombosis-coronary)
• Epinephrine: given after first or second defibrillation attempt, then every 3–5 min

Let $Q=(4t, 2t^2)$ be a point on $x^2=8y$ (using parametrization $x=4t, y=2t^2$). $O=(0,0)$.

$P$ divides $OQ$ in ratio $1:3$: $P=\left(\frac{1\cdot4t+3\cdot0}{4},\frac{1\cdot2t^2+3\cdot0}{4}\right)=\left(t,\frac{t^2}{2}\right)$

Let $P=(h,k)$: $h=t$ and $k=\frac{t^2}{2}=\frac{h^2}{2}$

So $h^2=2k$, i.e., the locus is $x^2=2y$.