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Home » But by how many times often means ratio. - Decision Point

But by how many times often means ratio. - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The function \( f(x) = rac{2x^3 - 3x^2 + x - 5}{x - 1} \) has a removable discontinuity. Find the value of \( f(1) \) after removing the discontinuity.

📌 \( 2x^3 - 3x^2 + x - 5 = (x - 1)(2x^2 - x - 5) \) using synthetic division.

📌 Cancel the common factor:

📌 \( f(x) = 2x^2 - x - 5 \) for \( x

📌 Evaluate \( f(1) \):

📌 \( f(1) = 2(1)^2 - 1 - 5 = 2 - 1 - 5 = -4 \).

📌 Thus, \( f(1) = -4 \) after removing the discontinuity.

📌 Find the area enclosed by the curves \( y = x^2 \) and \( y = 4x - x^2 \).

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