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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.
Tangents with Parametric Equations In this part we want to find out the tangent lines to the parametric equations given by X= f (t) Y = g (t) To do this let's first r
Let R be the relation on Z + defined by aRb iff gcd(a; b) = 1 (that is, a and b have no common divisors greater than one). Explain whether R is reflexive, irreflexive, symmetri
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Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?
Assume that i) Determine all the roots of f(x) = 0. ii) Determine the value of k that makes h continuous at x = 3. iii) Using the value of k found in (ii), sh
The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field
Describe Simplifying Fractions with example? When a fraction cannot be reduced any further, the fraction is in its simplest form. To reduce a fraction to its simplest form, div
2*8
What is a Computer? A computer is an electronic device which senses or accepts input data, performs operations or computations on the data in a pre-arranged sequence
Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear. DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like
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