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1) To allow random access to elements - Imagemakers

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 A = \left[ 2x^2 - \frac{2}{3}x^3 \right]_0^2 = \left( 2(2)^2 - \frac{2}{3}(2)^3 \right) - \left( 2(0)^2 - \frac{2}{3}(0)^3 \right).

📌 Calculating each term:

📌 = \left( 8 - \frac{16}{3} \right) = \frac{24}{3} - \frac{16}{3} = \frac{8}{3}.

📌 \boxed{\frac{8}{3}}.

📌 Find the remainder when \( v^4 + 3v + 1 \) is divided by \( v^2 + 1 \).

📌 To find the remainder of \( v^4 + 3v + 1 \) when divided by \( v^2 + 1 \), express the division as:

📌 v^4 + 3v + 1 = (v^2 + 1)Q(v) + R(v),

📌 where \( R(v) \) is the remainder and has degree less than 2, so let \( R(v) = av + b \).

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