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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.
how can we prove that an absolute convergent series is convergent but the converse is not true.
Integration of square root of sin
Find out some solutions to y′′ - 9 y = 0 Solution We can find some solutions here simply through inspection. We require functions whose second derivative is 9 times the
How do you find the ratio for these problems?
Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini
Find the solution to the following system of equations using substitution:
what is the are of a square that is 2 inches long and 2 inches wide?
If the minute hand of a big clock is 1.05 m long, find the rate at which its tip is moving in cm per minute.
Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally
Regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
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