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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.
limit x APProaches infinity (1+1/x)x=e
Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 Ans: a 1 = 2, b 1 = 3, c 1 = 7 a 2 =
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
A man is known to speak truth 3 out of 4 times.He throws adie and reports it is a six. Find the probability that it is actually a six. Solution) we can get a six if a man s
E1) How is the 'comparison model' different from the 'complementary addition model'? E2) Create one word problem related to the children's world for each of the 4 models liste
: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.
Here are four problems. Four children solved one problem each, as given below. Identify the strategies the children have used while solving them. a) 8 + 6 = 8 + 2 + 4 = 14 b)
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
For the layman, a "function" indicates a relationship among objects. A function provides a model to describe a system. Economists refer to deman
Continuous Uniform Distribution Consider the interest earned on a bank deposit. Let X equal the value after the decimal point. (Assume no rounding off to the nearest paise.) Fo
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