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📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Question: A deep-sea microbial population grows such that the number of organisms at time $ t $ is modeled by

📌 N(t) = \frac{t^3 + 2t^2 - 5t + 6}{t - 1}.

📌 Find the remainder when $ t^3 + 2t^2 - 5t + 6 $ is divided by $ t - 1 $.

📌 We are asked to find the remainder when

📌 f(t) = t^3 + 2t^2 - 5t + 6

📌 is divided by $ t - 1 $.

📌 By the **Remainder Theorem**, the remainder is simply $ f(1) $.

📌 f(1) = 1^3 + 2(1)^2 - 5(1) + 6 = 1 + 2 - 5 + 6 = 4.

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Take the limit as \( n \to \infty \):
\lim_{n \to \infty} \left( \frac{1}{n} - \frac{1}{5n^5} \right) = \lim...
Both terms approach 0:
\lim_{n \to \infty} \frac{1}{n} = 0 \quad \text{and} \quad \lim_{n \to...
\lim_{n \to \infty} m_n = 0 - 0 = 0
The limit of \( m_n \) as \( n \to \infty \) is \(\boxed{0}\).
---Question: The average of $ 3v + 7 $, $ 5v - 4 $, and $ v + 10 $ is
Solution: To find the average of the three expressions, we first add t...
Now, divide the sum by 3 to compute the average:
\frac{9v + 13}{3} = 3v + \frac{13}{3}

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