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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.
Divergence Test Once again, do NOT misuse this test. This test only says that a series is definite to diverge if the series terms do not go to zero in the limit. If the
Solve the inequation: |x|
why arcsin(sinq)=pi-q [pi/2 3pi/2]
what is the difference between North America''s part of the total population and Africa''s part
1 1/3:2/3:1/6
There is a staircase as shown in figure connecting points A and B. Measurements of steps are marked in the figure. Find the straight distance between A and B. (Ans:10) A ns
#question.Mai is 3 years ypunger than twice the age of her brother .If b represents .
A compound fraction is a fraction that has other fractions inside its numerator or denominator. Here's an example: While compound fractions can look really hairy, they're r
how can you tell qhich trangle is sss,asa, sas, and aas s
A local pizza shop sells large pies for $7 each. If the cost of the order is proportional to the number of pizzas would they charge a delivery charge per pizza or per order ?
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