### Mathematics - Calculus - Minimization

An open-topped cylindrical pot is to have volume 125in^3. What dimensions will minimize the total amount of material used in making this pot? Neglect the thickness of the material and possible wastage.

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An open-topped cylindrical pot is to have volume 125in^3. What dimensions will minimize the total amount of material used in making this pot? Neglect the thickness of the material and possible wastage.

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Please help me in attached problems. A customer ordered a quadratic metal sheet with side length x0=10cm. What is the maximal acceptable error of the side length if the area of the metal sheet should be?... For each of the following functions: state if the function is monotone Decide if it is injective, surjective or bij

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Theorem: Suppose that a sequence S of real numbers has a subsequence that converges to a real number a. Then S converges to a. I know this is true as an if and only if statement, but I need a counter example to show that just one converging subsequence isn't enough. Here are two sequences I'm considering: {1,-1,1,-1,1,-1..