Theorem (Lebesgue dominated convergence theorem) Let {f} be a sequence of mea- surable functions converging in measure to f. If there exists a non-negative summable function such that f(x) ≤ (x) a.e. on E for each n = N, then lim fn(x)dx=ff(x)dx. 11-00 E

Q: Consider the following linear program: maximise Z =1.5x+y subject to: x<4 ys6 x+y<=5 X,y2 0

A: Given: Maximize z=1.5x+ySubject to:x≤4y≤6x+y≤5x, y≥0

Q: The eigenfunctions for y"- 2y' + Xy = 0, y(0) = 1, y(1) = 0 are o {c* sin(nrx)} 1 o {e sin(")}-1 100…

A: First condition should be y(0)=0, from the given answer there is no option such that y(0)=1.

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A: x1ι=x12-x22x2ι=1- x1x2x1(0)=2 and x2(0)=1Hence at  (2,1)x1ι=4-1=3x2ι=1-2=-1

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A:

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Q: The general solution of y" + 3y' – 10y = 0 is %3D

A: From the given problem,   y''+3y'-10y=0d2ydx2+3dydx-10y=0D2+3D-10y=0   So, the auxiliary equation…

Q: The x coordinates of the points of intersection between the two curves y = I* and y =-I + 12z are

A: Given : y = x2y = -x2 + 12x

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A:

Q: P(0 < z< ) = 0.2995 a. %3D b. P(-1.1 < z < 0.8225 с. Р( <zS 2.18) = 0.7044

A: Given that  Z follows standard normal distribution  Note: According to bartleby experts question…

Q: In triangle ABC, AB| = |AC] (as shown in the figure below). |BD| = |DC| and BE]> CE]. Suppose that…

A:

Q: suppos e Fx (x)= 2% , o<x<77, and 72 y = sing . find fyld) and Fyly) .

A: We are given a PDE in variable x as : fx(x) = 2x/π2 And we have to calculate the PDE : fy(y) w.r.t…

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Q: Which number is equivalent to A 2 B 9 C D 81 729

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Q: Let K be the field of complex numbers G (KF) and fixed field of G (KF).

A:

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Q: what is the volume of this shape? please show work.!

A: Given: