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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.
Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved
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Equation for the given intervaks in the intervaks, giving ypout answer correct to 0.1 1.sin x = 0.8 0 2. cos x =-0.3 -180 3.4cos theta- cos theta=2 0 4. 10tan theta+3=0 0
Differentiate following functions. Solution At this point there in fact isn't a lot of cause to use the product rule. We will utilize the product rule. As we add
Give an example of Divisibility? If you can divide one number by another without getting a remainder, we say that the first number is divisible by the second. For instance, the
how does sin of x equal negative 1/3
Find the GCF of 70 and 112
For a first order linear differential equation the solution process is as given below: 1. Place the differential equation in the correct initial form, (1). 2. Determine the i
use an expression to write an expression with five 3s that has a value of 0
A plane is flying at 200 mph with a heading of 45degrees and encounters a wind mph from the west. What is the velocity and heading?
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