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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.
Recognizes the absolute extrema & relative extrema for the following function. f ( x ) = x 2 on [-1, 2] Solution: As this function is simpl
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If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected".
calculate the shortest distance between A and B 40degrees west and 50 degrees east respectively laying along 57 degrees north
how do i write a conjecture about the sum of two negative integers.
tanx dx
I need to simple this rational expression, but I can''t figure out how. (x+1)/(x^2-2x-35)+(x^2+x-12)/(x^2-2x-24)(x^2-4x-12)/(x^2+2x-15)
Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers. Examples of numbers whic
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