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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.
1/cos(x-a)cos(x-b)
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le
what to do
if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 => 1/x 2 +5x+6 = 2/ x 2 +8x +15 => On solving we get x
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Derivative and Differentiation The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is de
I would like to know what a symbol in my homework means?
Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest
what is classification and how can you teach it?
i have this data 48 degree, 72 degree, 43.2degree, 24degree , 40.8degree on this make a pie chart
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