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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.
alternate segment theorum
Chi-square hypothesis tests as Non-parametric test(X2) They contain amongst others i. Test for goodness of fit ii. Test for independence of attributes iii. Test
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Find out if the following sets of functions are linearly dependent or independent. (a) f ( x ) = 9 cos ( 2 x ) g ( x ) = 2 cos2 ( x ) - 2 sin 2 ( x ) (b) f
Arc Length and Surface Area Revisited We won't be working any instances in this part. This section is here exclusively for the aim of summarizing up all the arc length and su
Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is
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Find the middle term of the AP 1, 8, 15....505. A ns: Middle terms a + (n-1)d = 505 a + (n-1)7 = 505 n - 1 = 504/7 n = 73 ∴ 37th term is middle term a 37
Application of rate change Brief set of examples concentrating on the rate of change application of derivatives is given in this section. Example Find out all the point
-6x-4y=-6 x+2y=-3
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