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Home » Fabric with Scissors: The Secret Hack Every Custom Crafter Is Using (Spot the Hidden Detail!). - Dyverse

Fabric with Scissors: The Secret Hack Every Custom Crafter Is Using (Spot the Hidden Detail!). - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Since \( x-1 > 0 \), \( x > 1 \), thus \( x = 3 \).

📌 The function \( f(x) = rac{2x^2 - 3x + 1}{x - 1} \) has a removable discontinuity. Find the value of \( f(1) \) after removing the discontinuity.

📌 Factor numerator: \( 2x^2 - 3x + 1 = (2x - 1)(x - 1) \).

📌 So \( f(x) = rac{(2x - 1)(x - 1)}{x - 1} = 2x - 1 \) for \( x

📌 Removing discontinuity, \( f(1) = 2(1) - 1 = 1 \).

📌 A sequence is defined recursively by \( a_1 = 2 \), \( a_{2} = 3 \), and \( a_{n} = a_{n-1} + 2a_{n-2} \) for \( n \ge 3 \). Find \( a_6 \).

📌 \( a_3 = a_2 + 2a_1 = 3 + 2(2) = 7 \)

📌 \( a_4 = a_3 + 2a_2 = 7 + 2(3) = 13 \)

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