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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.
Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans: sum = 2 √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )
how do you differentiate sinx/ex?
Example of Probability: Example: By using a die, what is the probability of rolling two 3s in a row? Solution: From the previous example, there is a 1/6 chance of
INTRODUCTION : Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this
Integrals Involving Roots - Integration Techniques In this part we're going to look at an integration method that can be helpful for some integrals with roots in them. We hav
A card is chosen at random from a pack of playing cards.what is d probability that it is either a heart or the queen of spades
4x+8=32
Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign. The meaning of this is that we can then say, 0 a n +
Finite Population Correction Factor Or Fpcf) If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard er
10000+9854
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