Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x? y? that can be inscribed in the ellipse - = 1 with sides parallel to the coordinate axes. 4 16 Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis. Length = Width = (Type exact answers, using radicals as needed.)

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A: The integration of the integrals is  1) 3x/sqrt(1+3x2) 2) [sec(4x)-1]2 3)1/[1+(5x+1)2]

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A: As we know that; The slope of tangent line to the given curve is equal to the derivative of the…

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A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

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A: According to our guidelines we can answer only one question or 3 subparts of a question, other…

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A: Dear learner, As per our guidelines we can provide the solution for first one only. Kindly post…

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A: Here we have to solve the given problem.

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A: Answer as follows

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A: In this question we have to find F'(x).

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A: Answer is in step 2.

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A: By Alternating series estimation series test : s=∑n=1∞(-1)nbn        1)  bn+1≤bn2)  limn→∞ bn=0Then…

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A: The objective of the question is choose the correct option.

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A: A detailed solution is given below

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A: To evaluate the given integral.

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