Let's analyze the given function [tex]\( s = \frac{300}{d} \)[/tex].
1. Understanding the function:
- [tex]\( s \)[/tex] represents the speed of the current in the whirlpool.
- [tex]\( d \)[/tex] represents the distance from the center of the whirlpool.
2. Behavior as [tex]\( d \)[/tex] changes:
- As you move closer to the center of the whirlpool, the distance [tex]\( d \)[/tex] approaches 0.
3. Analyzing the limit as [tex]\( d \)[/tex] approaches 0:
- We need to find the limit of the function [tex]\( s \)[/tex] as [tex]\( d \)[/tex] approaches 0.
- Mathematically, we are looking for:
[tex]\[
\lim_{{d \to 0}} \frac{300}{d}
\][/tex]
4. Evaluating the limit:
- As [tex]\( d \)[/tex] gets smaller and smaller (approaches 0), the denominator of the fraction becomes very small.
- When we divide a constant number (like 300) by a very small number, the result becomes very large.
- Hence, as [tex]\( d \)[/tex] approaches 0, [tex]\( \frac{300}{d} \)[/tex] increases without bound.
5. Conclusion:
- The speed [tex]\( s \)[/tex] approaches infinity as [tex]\( d \)[/tex] approaches 0.
Therefore, the correct statement is:
- As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
