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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.
On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.
shape
In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist. Consider the differential equation y′′ + p (t ) y′ + q (t
express each logariths in terms of log3 P and log3 Q. 1. log3 P^2 Q^3
1
Method of cylinders or method of shells The formula for the area in all of the cases will be, A = 2 ∏ ( radius ) (heig
5/7+5/14
Q. Explain Binomial Distribution? Ans. The binomial distribution occurs when you are considering the probability function of a binomial experiment. Binomial Experiment
the size of my sitting room is 7metres by 6metres . i bought a rug for covering the centre of its floor. one metre of the floor around the edge of the room is not to be covered by
what is derivative
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