Given the function fx,r(x,y) ) = {(x² + y²) / 8 [(x² + y²)/8π x² + y²
Q: dy Find da if y = In(xiV1+ z° dy %3D dx
A: Recall: d(u.v)dx= u dvdx+dudx v d(xn)dx= n xn-1 d(ln x)dx=1x
Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…
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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…
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Q: Assume that X and Y have joint pdf Sr + 3x?y if 0 <r<1 and 0 < y < 1, f(x, y) = %3! otherwise.
A: We know that, Covariance(X,Y) = E(X).E(Y) - E(XY) Here E(X) and E(Y) are given so we'll Calculate…
Q: • !!! 622 dV where G is bounded by x + 2y + 4z = 8 in the first octant. 3. Evaluate
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Q: x + y The joint pdf of X and Y is fxy(x, y) = 3 0 a) Determine E[Y|x=1] b) Determine E[Y|x=0] 0<x<2,…
A: Method: find the marginal and tuen conditional pdf.
Q: Evaluate ſƒ ƒ(x, y, z)dS for f(x, y, z) = x and S is the cylinder x² + z² = 16 for 0 ≤ y ≤ 2.
A: Given: fx, y, z=x and S is the cylinder x2+z2=16 for 0≤y≤2. We have to evaluate ∫∫Sfx, y, zdS.
Q: a) V.VXA-o, b) VX V-D-O マ×(マ×ズ)= マ(アオ)ー ブイ )v(ズx2)=でしマメズ)ーオ(マ×ご) %3D
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Q: 1. Let f(x, y) = x cos (x²y). find: af a) ƏH b) of evaluated at (s) our (show you work)
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Q: Evaluate |//.(a (x + y – 5z) dV where E = {(r, y, z) | - 4< y< 0,0 < I < y,0 < z < ¤ + y³} E Round…
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Q: 1 Сompute L f dx, where f(x)=|x|.
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Q: Evaluate the integral •1 •1 I * min(r, y) dy dr, where min(x, y) is the minimum value of x and y.
A: As min(x, y) is not given so here two cases arise. Case (1) min(x, y) = x Therefore, ∫01∫01x…
Q: Determine k, so that ƒx¸y(x, y) = a) Determine E[Y] kx 0 0<x<y<1 otherwise is a joint pdf.
A: Given function is fX,Y(x,y)={kx 0<x<y<10 otherwise
Q: aL d( aL (i = 1,2, ,n) ... aq, dt dg,
A: We have to prove given result:
Q: (2) Let x, y E R. Then: (a) 3r€ Q3 x <r<y, (The Density theorem of the rational numbers). (b) 1* 3z€…
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Q: The double integral ſf f(x,y) dA is always positive. R
A: The given statement, the double integral ∬Rfx, ydA is always positive. We have to determine whether…
Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…
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Q: üx (u x i) = 0 for all u, v in R.
A: we have to identify the given statement is true or false
Q: Let f(x,y) = K (x² + y²) IA (x,y) where A is the region bounded by y=1x1 and y=2. Find K so that *…
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Q: Set up an integral for the circulation of F along the curve C, where F = (x² + y², x² - y²) and C is…
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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False
A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.
Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…
A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.
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- Given f(x, y, z) = x² – 6y- 4z', evaluate the following: af af af azLet f EBV (Co,1]). Define F(x) = √ ["f(t) dt, x € (0,1], Sta Lo, x = 0. Show that F E BV([0.1).Let g(x, y) represent the density of gold deposits in units of kilograms per square kilometre near a windmill, where the coordinates a and y are measured in kilometres east and north of .1 .1 the windmill respectively. Which of the following must be equal to g(x, y) dæ dy? 0 1 :7J g(x, y) dz dy -1 1 .1 1 || g(2, y) da dy + I g(2, y) dæ dy -1 1 2 | g(x, y) dy dæ 0. O All of the above O None of the above
- Please provide a detailed and complete solution. Thank youIf u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2Suppose that a) b) f(x, y) = [15x²y ; 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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