111 (x+y3z) dV where E = {(x, y, z) | -2 ≤ y ≤0,0≤x≤y, 0

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t.…

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Q: pYq (pA-q) V (-p ^ q) Show that each of the following holds. a. p ≤ p = 0 b. pvp = I

A: Let's prove each of these statements: (a):  To show p⊽p≡0: We'll first express p⊽p using the…

Q: S(x)dt, iff(x)= Vx-k+1;k-13x< i, k=1, 2.n.

A: By substitution, we calculate the following Integral.

Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: 3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

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Q: 19. Evaluate 2 2+x2+x+y SS S f(x,y,z) dzdydx where f(x,y,z)=4. 0 0 0 Answer: 112

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Q: Find x²dA where R R = } {(x, y) | 4x² + 16y? < 64

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Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: for z = In(2® + y*). Find

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: O x = 4 ve Find all points where the function is discontinuous. e

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Q: 31 Xi + 47 Xz + 14X3 Ex Al+

A: Given: Max z=31x1+47x2+14 x3Subject to; 2x1+3x2+x3≤4 and x1, x2, x3≥0 To find: Optimal solution and…

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A: Here we have to evaluate I=∫xex1+exdx ...........................(1)

Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: 10) s) =-2 -2

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Q: Se xye" dy, C. x- , y-, z- , 0 <te1

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Q: 1-ス 17+4 キ文T AND FIMD

A: Given that:x=t+t-1 and y=t2+t-2

Q: sech x dx , 0 < x < 1

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Q: Q/ Let x~P(m) and let y = 5x , find the p.d.f of y

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Q: The Valne of x For V50+7x <x+8.

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Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: Let z = 6exv , find dz %3D

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Q: Let f(x, y) = e"r³ Evaluate f(3, 0)

A: The function of two variables  x and y will be of the form,   The function value of this kind of…