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Q: f z x dA, D= {(x, y) |0 < x < m, 0 < y< sen x} 9. D 10. | x dA, D= {(x, y) |1 < x < e, 0 < y< In x}…

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Q: Find the most general antiderivative. O se3x + 9eX + c 3 e 3x + 9eX +C Z3x - 9e* + C 7 e 1 3x ex. +

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Q: "I INAICATE If THtE fOLLUWINh SRRZES ConveilCE OR DeveRしe。エ0ENTICY Tésrs Uszo. TESTS HT in (4nt -n)…

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Q: dz If z = x² y', x = 3, y = t then =? dt Select one: O 613 + 312 O 1 O 2712 O None of them

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Q: a of the following juncions. s- 1 (b))F(s)% = %3D 2s2 -8 s + 11

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Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1

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Q: OVIS lhigaimad goinisab A awordz n El 2nibs to s(t) milov ad sd osvig 2000 W x(t)

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Q: Evaluate * ISS 9z dV E where E is enclosed by z = x? + y? and z = 1 4JT O 3T O 27 ол

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Q: Determine L '{F}. s?F(s) s+5 + 3sF(s) – 10F(s) = %3D 2 s+ 6s

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Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: 3. Let F lt) be the antider¡vatPve of f (t) the most general antiderivative of flt>= 8 sec?(t) -92

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Q: . Find x(t) = Σo ant such that tx" = x' for t > 0 when x(1) = 0 and x'(1) = 1. in=0

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Q: Let XN(3, 4) and let Y~ N(2, 3). Define S = X + 3Y, where 'X and Ya atistically independent RVs.…

A: Given that: X~N3,4Y~N2,3S=X+3Y, X and Y are…

Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: If f(x, y) = (xy)", with |xy| < 1, find 2 af af and n=0 fe -y/(1-xy)^2 af -x/(1-xy)^2 dy

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Q: 1: Let w = eVE, where x = 5s2 – 4,2, y = 3r?s?, and : = Find the value of when s = 1 and r = 2.

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Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: a)-What is fof g ofh 3)? fari= gal= bprove f:R¬R fer )=4lis not Surgective and is not injective.

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Q: 2) H. GN H G'N H' %3D in HUG b. (GUHY %3D e

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Q: Let D={(x,y,z) : x2+y2+z?s 49, z2 0}. Evaluate z dv.

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Q: 3.Evaluate ex dx, by Simpson's ½ rule. n=6` 1 = (b − a) ƒ (xo) + 4f (x₂) + 6 f(x₂)

A: We have to solve by Composite Trapezoidal Method.

Q: f(z) =z2 is discontinuous in C

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Q: f(z) dz where a inside r= Z-a 2ni O 2nif(a) O 10

A: Using Cauchy integral Formula:

Q: Sz Evaluate j dz j dz Ţ eª* dy.

A: Use change of order of integration tonsolve it.

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: Q: If f(x)= ax* + withE a, > 0, b >0 +b,x + b, then show that Lt f(x)=o ifn>m. %3D

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Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: Given a J.p.f of x and y as f(x,y) = {x+y for 0<x<1,0<y<1, 0 O.W then the mean of x and y ( E(x, y)…

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Q: al HL b7 SAS C) NOt Co ng ruent

A: We will prove what relationship these two triangles have.

Q: Find the following antiderivatives. 49 – 24 dy 44 +1 (a) / : (b) / tan u + tan u du Vtan? u – 2

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: 6. Write.a.Ct).in. the farm..aaT.T+ a. N. a..r(t).=(tcost). .+ (tsint.) j.+t ..to.

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Q: S dy ² + 4y+20) ²

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Q: a?u du k 00 at Subject to the condition u(0, t) = 0, u(L, t) = 0 50x u(x,0) = f(x) = 50 – L. 0<x<L

A: Please check step 2 and 3 for solution

Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: For testing H,: M=M, V.S H;: M2.546)=0.01, then the p- value is اختر احدى الدجابات 0.99 0.1 X 0.9…

A: Statistical hypothesis testing is an important method in inferential statistics. It is used to test…

Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: f(z) = z is discontinuous in C ulgn O İhi O

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Q: -f L[te cost] = O A. %3D (5+ 1)² +1] (s+ O B. * + 25 +. +1

A: We have to find the Laplace transform of the given function.

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: [D] Evaluate det (A), where 0 0 a u b 0 A = v w с 0 2 d

A: Let's find.

Q: Q/ z = x + f(a) and a = ry. Show that: 尝-端=

A: We use the definition of partial derivatives to prove the given result.

Q: 1 (스 est An Fis)=t n(1+) cSst e's e

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

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Q: Evaluate ſ dz j d ſ e dy. O 8/3 O 8e-8 O 8e/3 O8

A: Explanation of the solution is given below....