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Home » #### \(100 - 25\pi\) - IX Labs

#### \(100 - 25\pi\) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \[ h(x, x) = \frac{x \cdot x}{x^2 + x^2 + 1} = \frac{x^2}{2x^2 + 1} \]

📌 Now assess the limit as \( x \to 1 \):

📌 \[ \lim_{x \to 1} h(x, x) = \frac{1^2}{2(1)^2 + 1} = \frac{1}{2 + 1} = \frac{1}{3} \]

📌 Thus, the limiting value is \(\boxed{\frac{1}{3}}\).

📌 A computational linguist uses a cubic model \( p(u) = u^3 - 3u^2 + 2u \) to analyze syntactic complexity. Determine the number of distinct real roots of \( p(u) = 0 \).

📌 We solve \( p(u) = u^3 - 3u^2 + 2u = 0 \).

📌 Factor out \( u \):

📌 \[ u(u^2 - 3u + 2) = 0 \]

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5**Question:** A herpetologist is studying a population of lizards in...
Solution:** To find the remainder when \( P(x) = x^4 - 5x^3 + 6x^2 + 4...
Here, \( c = 2 \). Calculate \( P(2) \):
P(2) = (2)^4 - 5(2)^3 + 6(2)^2 + 4(2) - 8
= 16 - 5 \times 8 + 6 \times 4 + 8 - 8
= 16 - 40 + 24 + 8 - 8
= 16 - 40 + 24

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