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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.
finding the vertex for the function of the form f(x)=ax^2+bx+c
Given f (x) =10x^3 - x^5 , find all intervals(in Interval Notation) of Concavity and the x-values of all Inflection Points.
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
The figure shows the sketch graphs of the functions
0.875 of a number is 2282. What is the number ?
Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r
ABCD is a trapezium AB parallel to DC prove square of AC - square of BCC= AB*
A toy company produces 2 models of water guns: spray king and zapper. They are manufactured in batches for easier packaging and sale. Two of the limiting resources are 1200 pounds
Ms. Mehta teaches in a government primary school in Delhi. The children who come to her in Class 1 are familiar with a few numbers. At the beginning of the session, she asks the ch
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