=Sdx + 5: Bx+C 19) S- A. 0, 1, 1 dx, then values of A, B and C respectively are %3! x(x +1) 2+1 В. -1, 1, 0 С. -1,0, 1 D. 1, -1,0

Q: S = {(x, y, z) E R : 2 = x² + y°, 0 s 4}. Evaluate e* dS. ds.

A: To evaluate the surface integral over the surface S is given by the equation z=gx,y, use the…

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: Calculate ∬Sf(x,y,z)dS For x^2+y^2=9,0≤z≤3;f(x,y,z)=e^(−z) ∬Sf(x,y,z)dS= ?

A: Find the parametric equation for the given curves.

Q: 3. A RV is described by: x+y 0<x<2,0< y<2 S(x,y) ={ 8 [0, otherwise. Find VAR((X+Y)/2)

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Q: 33]x = C],B = [] then, 4,l = f A = %3D 1. 16 2. 4 3. S 4. - 12

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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: 5 2 11 what is 3 Given that f(æ)dæ : f(s)ds?

A: We will use the following 2 properties of definite integrals to find the answer

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: S6xw, fx,w (x, w) = 0, 0sxs 1,0 < w s Vã otherwise (3x2, fx(x) = lo, 0<x<1 otherwise

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Q: 18. X ve Y bağımsız r.d. ler olsunlar. E(X)=3, E(X²)=25, E(Y)=10, E(Y² )=164 ise Var(3X-Y- 8)=? a.…

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Q: A dice is rolled twice. Let X equal the sum of the outcomes, and let Y equal the first outcome minus…

A: In probability theory and statistics, covariance measures how two random variables are jointly…

Q: If y(s)=1/(s2-3s+2) , and y(t)=L-1(y(s)) , then y(1)=? (a) e2-e

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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: (d) VX € P(N), XCR. (e) In ɛ N, VX e P(N), |X| < n. (f) Vn e Z, 3X c N, |X| = n. (g) 3me Z, Vn € Z,…

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Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: PLEASE HELP ME ANSWER WITH SOLUTION    18

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Q: الرابع: جد ناتج احد التكاملين التالي ين 1- Smte) xy e*y° dxdy 2- r? N4-y² ry8-x²-y" zdzdxdy x²+y2 2-…

A: 1 ∫01∫0ln(2)xyexy2dxdy first we will solve ∫0ln(2)xyexy2dx ∫0ln(2)xyexy2dx=y∫0ln(2)xexy2dxSubstitute…

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

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Q: 10 8. If S" f(x)dx = 4 and Siof(x)dx = 7, then ſ, f(x)dx = -3 %3D 10 (a) 0 (b) – 3 (c) 3 (d) 11

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Q: Let cov(X,Y) = var(X) = and h(y) = }* (4y, 0<y<1 %D %3D 45 45 elsewhere Then the value of var(2X +…

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Q: d.A, A = {(x; y) E R² : y € [0, 1], x € [y², e-]}

A: Given: I=∫∫A1x34dA   A=(x,y)∈R2: y∈0,1, x∈y2,e-y

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

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Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: E=D{(r,0,2): 0s es n, Os zs 1, Vzs rs 1.

A: Given,          E=r, θ, z : 0≤θ≤π, 0≤z≤1, z≤r≤1 To find:           ∫∫∫Ey2ex2+y23dV

Q: f(x, d,Z)cbxcly dz

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Q: Show for R(t) = e?-t and S(x) = 2x + 1, that (Ro S)(x) = e1²+2#.

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Q: The evaluation of S xy e*dxdy is 0.5 e 0.25 e- 0.5 O e-0.25 O

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Q: B = {(x,y xs2, -a sy s3, 0£21} SS, x*yz²dV 2 'B

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Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: (4) Evaluate : S[(xy? + yz') dV if Q = {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 21}

A: Note: As per our company guidelines we are supposed to answer only one question at a time. Kindly…

Q: What value of c will satisfy y(x) = c(1 – x²) given y(0) = 1? 2 O Option 1 Option 2 3 Ontion 3…

A: Let's find.

Q: 1-find the value of z and x, 2- find (A") + d* (x². e3*) 3- find (A+ 3 lm 3), 4- 2A*A", 2r + Z+ y= 2…

A: Given: The equation are  2x + Z + y = 2 x - Z + 4y = ln 1 x + 2y - 2z = 4

Q: Calculate ffs f(x, Y, z) dS For x? + y? = 16, 0 <z< 7; f(x, y, 2) = e Sls f(x, Y, z) dS 4pi(1-e^-7)

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Q: S = {(r, y, z) E R³ : 2? = x² + y°, 0 s< 4}. %3D Evaluate e dS.

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Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: e |/ (x² + y³) dV, where E = {(x, y, z) E R³ : VA- x² – y? <z< V9– x² – y?}. Evaluate E

A: The region E will be bounded within the upper half of the spheres x2+y2+z2=(3)2 and x2+y2+z2=(2)2.…

Q: 39. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Az and dz.

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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: [F(x, х, х, х) — х] (х— х) — b K5 x- e-d <{x- [Ks – 1] (e– d) S {* x (е- d) [Кз — 1]—Ь e- d | | 1…

A: Algebraic identity: Algebraic identity for the square of the difference of any two algebraic…

Q: In Exercises 4-15, find the minimum and maximum values of the functionsubject to the given…

A: Consider the function fx,y=2x+3y with constraintsgx,y=x2+y2=4

Q: Find f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: (a) Vx €R, if x=-1, then x--I (b) 3x €Za vy e Z. (x+y)= (c) Vm, Vn € Z, if m+n is even, then m is…

A: Given:- a) ∀x∈R , if x2=-1,then x4=-1 b)∃x∈z∋∀y∈z(x+ y)5=x5+y5 c)∀m,∀n∈z , if m+ n is even, then m…

Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

A: