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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.
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
y+7 3y-2 --- = 1 + ---- 3 5
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
what is the difference between North America''s part of the total population and Africa''s part
Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0 y (3) = 6 y′ (3) = -1 We can wri
Here we learn: 1) Discussed what counting means, and stressed that it is not the ability to recite number names. 2) Talked about the need for a child to understand several pr
How to get the answer
Q. Define Multiplication Rule in probability? Ans. A family has two girls, Ann and Barb, and three boys, Carl, David and Earl, in it. In how many ways can the mother pick
how to curve trace? and how to know whether the equation is a circle or parabola, hyperbola ellipse?
Write following in terms of simpler logarithms. (a) log 3 (9 x 4 / √y) Solution log 3 (9 x 4 / √y) =log 3 9x 4 - log y (1/2) =log 3 9 + log 3 x 4
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