A rectangular base box must be constructed, with a sheet of cardboard 40 cm wide and 50 cm long, removing a square from each corner of the cardboard and folding the resulting sides perpendicularly. Determine the size of the side of the square that allows you to build a box of maximum volume. Answers: 7.48

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A: As per the instruction, we will be answering the first question. Given:

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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Q: Evaluate lim (x) x-0 f(x) . . . . . . . . . . . F . . y 4 f(x) g(x) X

A: See this solution in below

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A: Here the region of integration is bounded by y=x, y=1, x=0, x=1. Plotting the region we have:

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