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why are my lips so dry - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 I''(t) = rac{(2 - 4t^3)(1 + t^3)^2 - (2t - t^4)(6t^2(1 + t^3))}{(1 + t^3)^4}.

📌 Factor \( (1 + t^3) \) from numerator:

📌 I''(t) = rac{(1 + t^3)\left[(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)

📌 ight]}{(1 + t^3)^4} = rac{(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)}{(1 + t^3)^3}.

📌 First term:

📌 Second term:

📌 -6t^2(2t - t^4) = -12t^3 + 6t^6.

📌 - 2t^3 - 4t^6 - 12t^3 + 6t^6 = 2 - 14t^3 + 2t^6.

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Discriminant: \( 35^2 + 4Ã2Ã102 = 1225 + 816 = 2041 \)
So \( x = rac{ -35 + \sqrt{2041} }{4} \) (since \( x > 0 \))
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#### \( rac{-35 + \sqrt{2041}}{4} \)
However, due to complexity, and since the user requested difficult Oly...
The sum of the first \( n \) terms of an arithmetic sequence is given...
The sum formula: \( S_n = rac{n}{2} (2a + (n-1)d) \)
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