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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.
Let's here start thinking regarding that how to solve nonhomogeneous differential equations. A second order, linear non-homogeneous differential equation is as y′′ + p (t) y′ +
Properties of the Indefinite Integral 1. ∫ k f ( x ) dx = k ∫ f ( x ) dx where k refer for any number. Thus, we can factor multiplicative constants out of indefinite integral
Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim
Prisoners Dilemma This is a type of non-zero sum game and derives its name from the given story: The district attorney has two bank robbers in separate cells and offers them
Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.
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HISTORY OF UNITARY METHOD
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