Test Course
Review: Allied supply issues
The Allies had some big problems with getting supplies during the war. They were moving forward quickly, but they didn’t have enough deep-water ports to bring in the necessary resources. They tried using the Normandy landing areas and ships directly on the beaches, but it wasn’t enough. The only deep-water port they had captured, Cherbourg, was destroyed by the Germans and took a long time to rebuild. They eventually took over the port of Antwerp, but it took a while to make it operational. They had to clear the area of enemy troops and naval mines. Because of these issues, there were disagreements between General Eisenhower and Field Marshal Montgomery about which army group should get priority for supplies. The Germans still controlled some major ports on the English Channel coast, and Dunkirk was under siege until the war ended in May 1945.
Review: Part 2
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Review: Part 3
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Review: Part 4
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Review: Part 5
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Course Outline
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Question: Find the derivative of the constant function \(f(x) = 5\).
Answer: \(f'(x) = 0\)
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Question: Compute the derivative of the linear function \(f(x) = 7x + 3\).
Answer: \(f'(x) = 7\)
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Question: Given the function \(f(x) = x^2\), find \(f'(x)\).
Answer: \(f'(x) = 2x\)
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Question: Compute the derivative of the function \(f(x) = x^3 – 4x^2 + x – 1\).
Answer: \(f'(x) = 3x^2 – 8x + 1\)
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Question: Find the derivative of the function \(f(x) = e^{3x}\).
Answer: \(f'(x) = 3e^{3x}\)
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Question: Calculate the derivative of \(g(x) = \sin(2x)\).
Answer: \(g'(x) = 2\cos(2x)\)
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Question: Differentiate the function \(y = x \ln(x)\).
Answer: \(y’ = \ln(x) + 1\)
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Question: Compute the derivative of \(f(x) = \cos(x^2)\).
Answer: \(f'(x) = -2x\sin(x^2)\)
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Question: Differentiate the function \(y = \tan(3x^2)\).
Answer: \(y’ = 6x\sec^2(3x^2)\)
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Question: Given the function \(f(x) = \frac{4x^3 – 3x^2 + 2x – 1}{x}\), find \(f'(x)\).
Answer: \(f'(x) = 4x^2 – 2x + 1 – \frac{4x^3 – 3x^2 + 2x – 1}{x^2}\)
