The cylinder x2+y2=1 intersects the plan x+z=1 in an ellipse

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The cylinder x2+y2=1 intersects the plan x+z=1 in an ellipse. The goal of this assignment is to find the point(s) on tha

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The cylinder x2+y2=1 intersects the plan x+z=1 in an ellipse. The goal of this assignment is to find the point(s) on that ellipse that is/are furthest from the origin. 1. Give a formula for the quantity to be maximized in terms of the (x,y,z) coordinates of the point. Hint: Maximizing the square of the distance is equivalent to maximizing the distance. 2. Identify the constraints and write down constraint equations. 3. Using the Lagrange multiplier method, find the coordinates of the point(s) on the ellipse which is or are farthest from the origin. Please show steps with as much explanations as possible. Thank you!

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