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Home » Highest powers: \(2^3\), \(3^2\) - Databee Business Systems

Highest powers: \(2^3\), \(3^2\) - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 v_3 = 1, \quad 0 = 0, \quad -v_1 = -1.

📌 Solving gives:

📌 v_1 = 1, \quad v_2 \text{ is free}, \quad v_3 = 1.

📌 Thus, \(\mathbf{v} = \langle 1, t, 1 \rangle\) for any real \(t\).

📌 \boxed{\langle 1, t, 1 \rangle \text{ for any } t \in \mathbb{R}}

📌 Find the range of the function \( f(x) = \frac{x^2 + 1}{x^2 - 1} \) as \( x \) ranges over all real numbers such that \( x \neq \pm 1 \).

📌 Let \( y = \frac{x^2 + 1}{x^2 - 1} \). Rearranging gives:

📌 y(x^2 - 1) = x^2 + 1 \quad \Rightarrow \quad yx^2 - y = x^2 + 1.

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