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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.
r=asin3x
what is a redtilinear figure? like what are for the requirments for a shape to be called that? example a regular polygon has all sides and angles equal. i cant find that kind of dr
If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
The dimensions of a rectangular prism can be expressed as x + 1, x - 2, and x + 4. In terms of x, what is the volume of the prism? Since the formula for the volume of a rectang
(3t-1)^4 (2t+1)^-4
how to divide an arc in three equal parts
There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a
Find the full fourier Series of e^x on (-l,l)in its real and complex forms. (hint:it is convenient to find the complex form first)
1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8
1. a) Find the shortest paths from r to all other nodes in the digraph G=(V,E) shown below using the Bellman-Ford algorithm (as taught in class). Please show your work, and draw t
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