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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.
4.2^2x+1-9.2^x+1=0
#31
Need help, Determine the points of inflection on the curve of the function y = x 3
1. Consider the code of size 4 (4 codewords) and of length 10 with codewords listed below. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1
Fundamental Theorem of Calculus, Part II Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =
Data collected from the STATS 10x class survey one semester included responses to questions on the number of different sexual partners and on the number of pairs of shoes the stude
HOW TO DRAW A TANGENT SEGMENTS TO A CIRCLE WHEN CENTRE IS NOT KNOWN?
5 years however, a man's age will be 3times his son's age and 5 years ago, he was 7 times as old as his son. Find their present ages.
What is Zero-Day Attack? Explain Zero-Day Attack
These can be expressed in terms of two fundamental operations of addition and multiplication. If a, b and c are any three real numbers, then; 1.
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