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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.
It is totally possible that a or b could be zero and thus in 16 i the real part is zero. While the real part is zero we frequently will call the complex numbers a purely imaginar
add 1 and 20 over 40 with 2 and 30 over 50
The distance around a square photograph is 12.8 centimeters. What is the langth of each side of the fotograph?
850ml is to be administered to a person over 8 hours using a drop factor of 20 drops/ml what is the flow rate in gtts/min ?
Calculate the linear equation: Example: Solve the equation 4x + 3 = 19 by transposing. Solution: Step 1. Transpose the 3 from the left-hand to the right-hand si
how is it done
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷dθ. Solution) Y=θ[SIN(INθ)+COS(INθ)] applying u.v rule then dy÷dθ={[ SIN(INθ)+COS(INθ) ] dθ÷dθ }+ {θ[ d÷dθ{SIN(INθ)+COS(INθ) ] } => SI
explain the basics of permutation
1+2+3+.....+n=1/2n(n+1)
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