To determine what happens to the density [tex]\( D \)[/tex] as the volume [tex]\( V \)[/tex] approaches 0, consider the equation given:
[tex]\[ D = \frac{13}{V} \][/tex]
Here, [tex]\( D \)[/tex] represents the density, 13 grams is the fixed mass, and [tex]\( V \)[/tex] is the volume of the substance.
1. Initial Observation: The equation shows that [tex]\( D \)[/tex] is inversely proportional to [tex]\( V \)[/tex]. This means that as [tex]\( V \)[/tex] changes, [tex]\( D \)[/tex] changes in the opposite direction.
2. Behavior as [tex]\( V \)[/tex] Approaches 0:
- When [tex]\( V \)[/tex] gets smaller and closer to 0, the denominator of the fraction [tex]\( \frac{13}{V} \)[/tex] becomes smaller and smaller.
- In the limit, as [tex]\( V \)[/tex] approaches 0, the denominator [tex]\( V \)[/tex] approaches 0.
3. Implication for Density [tex]\( D \)[/tex]:
- Since the numerator 13 is a positive constant and does not change, reducing [tex]\( V \)[/tex] to a very small value results in dividing 13 by an increasingly tiny number.
- Dividing by a number very close to zero results in a very large number because any positive number divided by a value approaching zero increases without bound.
Therefore, as the volume [tex]\( V \)[/tex] approaches 0, the density [tex]\( D \)[/tex] approaches infinity. This can be phrased succinctly as follows:
As the volume [tex]\( V \)[/tex] approaches 0, the density [tex]\( D \)[/tex] approaches infinity.
