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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.
120
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
three years ago,Rica was thrice as old as dandy.Three years hence,she will be twice as old.Find their present.
1-tan^2 A/1+tan^2 = cos A - sinA/cos A
Constrcut the adjacency matrix and the adjacency lists for the graph G belowr.
Dot Product- Vector The other topic for discussion is that of the dot product. Let us jump right into the definition of dot product. There is given that the two vectors a
Explain Multiplying/Dividing Negative Fractions? There are 3 steps to multiplying or dividing fractions. 1. If any negative signs are present, place them next to the numerator
A number of the form x + iy, where x and y are real and natural numbers and is called as a complex number. It is normally given by z. i.e. z = x + iy, x is called as the real part
Why is it important the the Enlightenment grew out of the salons and other meeting places of Europe? Who was leading the charge? Why was this significant? Where there any names or
how do you find the perimeter of an equalateral triangle
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