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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse
x2 + xy + y2 = 3.
Hints: (i) Use x2 + y2 as your objective function; (ii) You can assume that the constraint qualification condition and the second order conditions are satisfied in this problem, as well as in problems 2 and 3.
Problem 2. Maximize f (x, y, z) = yz + xz subject to y2 + z2 = 1 and xz = 3.
Problem 3. (a) Maximize f (x, y) = x2 + y2 subject to 2x + y ≤ 2, x ≥ 0 and y ≥ 0.
(b) Use the Envelope Theorem to estimate the maximal value of the objective function in part
(a) when the first constraint is changed to 2x+ 9/8y ≤ 2, the second constraint is changed to x ≥ 0.1,and the third to y ≥ -0.1.
(x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is
A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w
p=0
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In this case we will require deriving a new formula for variation of parameters for systems. The derivation now will be much simpler than the when we first noticed variation of pa
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