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Home » Evaluate the limit \( \lim_x \to 2 \fracx^2 - 4x - 2 \). - Get link 4share

Evaluate the limit \( \lim_x \to 2 \fracx^2 - 4x - 2 \). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 u^2 + 1 = 3u \quad \Rightarrow \quad u^2 - 3u + 1 = 0.

📌 u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.

📌 So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).

📌 Now recall \( u = rac{x+y}{x-y} \). Let \( r = rac{x}{y} \), assuming \(y

📌 e 0\). Then:

📌 rac{x+y}{x-y} = rac{r+1}{r-1}.

📌 Set this equal to each value of \(u\):

📌 Case 1:** \( rac{r+1}{r-1} = rac{3 + \sqrt{5}}{2} \)

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