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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.
ABC is a triangle right angled at c. let BC=a, CA=b, AB=c and lrt p be the length of the perpendicular from C on AB. prove that cp=ab and 1/p2=1/a2+1/b2
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Power rule: d(x n )/dx = nx n-1 There are really three proofs which we can provide here and we are going to suffer all three here therefore you can notice all of them. T
Mrs. Farrell's class has 26 students. Just 21 were present on Monday. How many were absent? Subtract the number of students present from the total number within the class to de
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Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures
Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution: S = {(H, H), (H, T), (T, H
Q) In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win
Kelli calls her grandmother every month. Every other month,Kelli also calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by the end
a local pizza store offers medium two-topping pizzas delivered for $6.00 per pizza plus a $1.50 delivery charge per order. on weekends, the store runs a game day special: if six or
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