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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.
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??
log8-log3
UNDETERMINED COEFFICIENTS The way of Undetermined Coefficients for systems is pretty much the same to the second order differential equation case. The simple difference is as t
Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves. Note also that we said "enclosed by" in place of "under" as we usually have
solve by factorization method; 10x-6y-3z=100, -6x+10y-5z=100, -3x-5y+10z=100
Measures of Dispersion - The measures of dispersion are extremely useful in statistical work since they indicate whether the rest of the data are scattered away from the mean
what is the difference between North America''s part of the total population and Africa''s part
Extended product rule : As a last topic let's note that the product rule can be extended to more than two functions, for instance. ( f g h )′ = f ′ gh + f g ′ h+ f g h′ ( f
One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti
what is solid geometry and uses of solid geometry
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