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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.
When 6 boys were admitted & 6 girls left the percentage of boys increased from 60% to 75%. Find the original no. of boys and girls in the class. Ans: Let the no. of Boys be x
How to solve Systems of Equations ? There's a simple method that you can use to solve most of the systems of equations you'll encounter in Calculus. It's called the "substitut
which shows the rate 12 inches of rain in 6 hours as a unit rate
Which expression below is equal to 5? The correct order of operations must be used here. PEMDAS tells you in which you should do the operations in the subsequent order: Pare
how do you identify area ??
Derivatives of Trig Functions In this section we will see derivatives of functions other than polynomials or roots of polynomials. We'll begin this process off through taking
What is log3(x+1)
1x1
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
applications of composit functions
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