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🧮 Calculus Problem
Let f(x) = 2x² - 1 and g(x) = x² + 3x
Calculate f'(x) and g'(x), then find f'(1) + g'(1)
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🧩 Logic Problem
If all A are B, and some B are C, can we conclude that some A are C?
Explain your reasoning with a proof or counterexample.
🔢 Sequence Problem
Find the next three terms in the sequence:
2, 6, 12, 20, 30, ...
Explain the pattern.
🚀 Vector Calculus
A particle moves along a curve defined by r(t) = (t², t³, t⁴). Find the velocity vector and acceleration vector at t = 2.
💡 Tricky Math Problem
A store offers a 20% discount on all items. If the original price of an item is $100, and there's an additional 10% tax after the discount, what is the final price? Show your work and explain why this is different from a 30% discount.
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