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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.
the adjacent sides of a parallelogram are 2x2-5xy+3y2=0 and one diagonal is x+y+2=0 find the vertices and the other diagonal
Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they
cot functions
Write down the system of differential equations for mass system and the spring above. Solution To assist us out let's first take a rapid look at a situation wherein both of
2+(+3)=
A fox and an eagle lived at the top of a cliff of height 6m, whose base was at a distance of 10m from a point A on the ground. The fox descends the cliff and went straight to the p
two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent
how do you find the length of a parallel line connecting two external circles of different sizes from the outside, given the value of both radius and one parallel line.
the formulas of the area of solid figures
General approach of Exponential Functions : Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential f
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