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Jan 27,2025

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Jan 27,2025

UpStudy AI · Accepted Answer

Calculate the limit $$ \lim_{s\rightarrow 5} \frac{s^{3}-125}{s-5} $$.
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
  $$\lim _{s\rightarrow 5}\left(\frac{s^{3}-125}{s-5}\right)$$
- step1: Reduce the fraction:
  $$\lim _{s\rightarrow 5}\left(s^{2}+5s+25\right)$$
- step2: Rewrite the expression:
  $$\lim _{s\rightarrow 5}\left(s^{2}\right)+\lim _{s\rightarrow 5}\left(5s\right)+\lim _{s\rightarrow 5}\left(25\right)$$
- step3: Calculate:
  $$25+25+25$$
- step4: Calculate:
  $$75$$
The limit of $$ \frac{s^{3}-125}{s-5} $$ as $$ s $$ approaches 5 is 75.
The limit is 75.

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