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Home » A. $ y(x) = (C_1 + C_2 x)e^2x $ - GetMeFoodie

A. $ y(x) = (C_1 + C_2 x)e^2x $ - GetMeFoodie

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \( x = 4 \) (since \( x > 2 \) for log to be defined).

📌 The graph of \( y = a \cdot 2^x \) passes through the points $ (0, 3) $ and $ (2, 12) $. Find \( a \).

📌 At \( x = 0 \): \( y = a \cdot 2^0 = a = 3 \).

📌 Check with \( x = 2 \): \( y = 3 \cdot 2^2 = 12 \), which matches.

📌 So \( a = 3 \).

📌 What is the remainder when \( x^4 - 3x^2 + 2x + 5 \) is divided by \( x - 1 \)?

📌 Use Remainder Theorem: evaluate at \( x = 1 \).

📌 \( 1^4 - 3(1)^2 + 2(1) + 5 = 1 - 3 + 2 + 5 = 5 \).

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