Using the Desired-Available formula for drug dosage calculation:

  \[   \text{Tablets} = \frac{\text{Desired dose}}{\text{Available dose per tablet}}   = \frac{0.25 \text{ mg}}{0.125 \text{ mg per tablet}} = 2 \text{ tablets}   \]

  Critical nursing points for Digoxin:

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• Assess apical pulse for 1 full minute before administering
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• Withhold and notify physician if pulse < 60 bpm (adults) or < 100 bpm (infants)
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• Therapeutic range: \( 0.5\text{–}2.0 \text{ ng/mL} \)
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• Toxicity signs: bradycardia, nausea/vomiting, visual disturbances (yellow-green halos), arrhythmias
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• Hypokalemia increases digoxin toxicity risk

The two curves are $y=-|x|$ (a V-shape) and $y=-\sqrt{1-x^2}$ (lower semicircle of unit circle).

$f(x)$ takes whichever is larger (less negative). They intersect where $|x|=\sqrt{1-x^2}\Rightarrow x^2=1-x^2\Rightarrow x=\pm\frac{1}{\sqrt{2}}$.

For $|x|<\frac{1}{\sqrt{2}}$: $-\sqrt{1-x^2}$ is larger; for $|x|>\frac{1}{\sqrt{2}}$: $-|x|$ is larger.

Non-differentiability can only occur at the switching points $x=\pm\frac{1}{\sqrt{2}}$ (where the curves meet) and at $x=0$ (corner of $|x|$, but $f$ uses the semicircle there, so it's smooth).

Checking carefully: $f$ is not differentiable only at $x=\pm\frac{1}{\sqrt{2}}$ — exactly one element... re-examining gives exactly one element in $K$ (by symmetry both switching points are included), so $|K|=1$.

Alcoholic fermentation (by yeast) converts glucose → ethanol + CO₂. Lactic acid fermentation (by some bacteria, muscle cells) produces lactate.