Please, I need only a written explanation and solution! Exam 9 Bonus Problem 2 (3 bonus points, CCOs #5 & 10)Consider a PDE for Y(x, t) with a boundary condition at the left boundary of the spatial domain 0 ≤ x ≤ L given bya²yax2(x 0,t) = cos(t).(2)If the spatial domain is discretized by a mesh of M equally sized intervals, give the discrete boundary condition at x₁ = 0 andt = t(n) that is at least second-order accurate in space, i.e., Y(n),Required submission:Handwritten or typeset solution including all solution steps;=

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q3) Show that the locus of extremum points (i.e., maximum and minimum, spinodal) of constant temperature curves (isotherms) in the (pr, vr) coordinate system for a van der Waals gas is given by the equation; Pr 2 v² Vi ده |
6. Determine the absolute maximum and minimum values of f(x, y) = 2x² + 3y² on the rectangular region where -1 ≤ x ≤ 1 and -1 ≤ y ≤ 1.
Find the absolute maximum and absolute minimum values of the function f(2, 3) = 2æ° + 3æy+ 2g over the coordinate axes and the closed region bounded by the line x + y = -1.
11) Find each of the two areas bounded by the curves y = x3-4x and y = x² + 2x. Points of intersection: (0, 0), (3, 15) and (-2, 0) (-2, 0) (-1.15, 3.08) A da (-1,-1) (3, 15) (1.15,-3.08)
Find the maximum and minimum possible areas bounded by the curve y(x) in the interval 0 ≤ x ≤ 1, subject to the constraint that Барах 1 48 and y(0) = y(1) = 1.
3. Find the absolute maximum and absolute minimum values of f(x, y) = x +xy+ y -3x+3y on the triangular region cut from the first quadrant by the line x+y= 4 (Sketch the region).
What is the correct answer
express the extreme value theorem for functions of two variables . find the absolute maximum and minimum values of f(x,y)=2x2-4x+y2-4y+1 on the triangle bounded by x=0, y=2 and y=2x.
8 Find the Minimum distance from the origin to the plane X+2y-z=5
1. Let C, denote the circle r +N=1 and consider the function F(, y) = r'(y- 1. (a) Suppose points are constrained to lie on C. Find the coordinates of all the constrained stationary points of Fand identify which, if any, are constrained maxima or minima. (b) Consider the region D that lies within C, and also satisfies y 20. Find the maximum and minimum of Fover the region D (including its boundaries), and give the coordinates at which these values occur. (c) Now let C, denote the circle + y for some ye R, and suppose points are constrained to le on C, Let (a, y) denote the coordinates of the maximum value of Fsubject to this constraint. By calcutating these coordinates when y is large, ahow that the ratio of a" and y" approaches a constant value a (independent of ) as
4:03 AA sment.education.wiley.com E KQ1123 - Tutorial 3 2 of 15 - / 4 View Policies Current Attempt in Progress Select the term that best describes the level curves for each of the functions f. f (x, y) = 3x²: f (x, y) = x² + 3y²: f (x, y) = y – 2x?: f (x, y) = 5x² – 5y²: eTextbook and Media Hint Save for Later ENM
Find the extreme values of the function f(x, y) = 2z² + 3y² on the circle ². +²=4 Use Lagrange multipliers; find f = Ag.: Answer format: Enter the value [for A, type \lambda or use the keyboard sign] Check Answer/Save Find fy= Agy: Step-By-Step Example Check Answer/Save Answer format: Enter the value [for A, type \lambda or use the keyboard sign] Step-By-Step Example Live Help Answer format: (a, b), (c,d), (e, f), (g, h) Live Help Solve the equations fz = Agz, fy = Agy, and a2 + y² = 4, and find all the (x, y) pairs: X

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