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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.
Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du, where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably
Properties Now there are a couple of formulas for summation notation. 1. here c is any number. Therefore, we can factor constants out of a summation. 2. T
what is the answer
log6 X + log6 (x-5) = 1
Teng is designing a house and in each room he can choose from tiles, floorboards, or carpet for the floor. a. How many combinations of flooring materials are possible if he designs
Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S
The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number
Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6 ⇒x/2= sin
I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.
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