1. Let E be the region in the first octant x 20, y ≥ 0, and z 20 that is bound by the plane 2x+y+z= 2. Evaluate the integral JJJ₂2-2x -y dv. ? 7/2

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Q: Evaluate one the integrals: B E b) cos(8x) x² +1 0 -dx

A: 1.If f(x)=p(x)q(x) and q(x) have only complex roots then ∫-∞∞f(x)dx=2πi[Sum of Residues of f(z) at…

Q: " The sum of the two power series: n(n + 2)cnxn-1 + Σ Enchanta 72=0 n=1 can be written in a single…

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Q: n n Let A = k², B=(k+1)², C = k₁ D = 1 and E=Ĺ5-k. Consider k=1 k=1 k=1 k=1 k=1 Σ(+48) (6-j)* j=1 a)…

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Q: Let T: V → V be a linear transformation, and suppose that A is an for T. Show that the set V₁ = {v €…

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Q: -14 Given that write 3 -5 -3 -14 ] -5 = 2 -2 -3 1 0 0 −1 −1 as a linear combination of the vectors 1…

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Q: Let f: R → R be defined by f(x) = 6 - 6x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) +…

A: Given that f:ℝ→ℝ be defined by fx=6-6x. We to find whether fis a linear transformation or not.

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A: The generating function of the given sequence ak is ax=13x4-1.

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Q: Let f(x) = for sin(t²) dt. Find f" (x).

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Q: -10 -10 Given that ¹0 f(x) dx = 5, ₁0 f (x) dx = −3, and f(x) dx = 7 determine the 12 100 -5 100…

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Q: 1. (a) The initial temperature of the finite rod 0 ≤ x ≤ is given by the function (x) = sin(2x). The…

A: From the given non homogeneous system we find the eigenfunctions and then undetermined Coefficients.

Q: 2. Let R be the shaded region that lies to the right of the parabola r= (y - 3)2 + 2, to the left of…

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Q: Let E and F be events in a sample space S with probabilities p (E)= and p (F) = such that the…

A: You have asked multiple questions. So I have solved the first question for you. For the remaining…

Q: EX: If f is the graph shown below and g(x) = f(t)dt, find the values of g(0), g(1), g(2), g (3),…

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Q: Using variation of parameters, solve the differential equation y" + 3y + 2y = sin(e*). (Hint: [ e²*…

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Q: Find all the eigenvalues and eigenfunctions for the following BVP: y"+Ay = 0, y (0)=0, y (π)=0 Draw…

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Q: ∞ n=1 In(n) 2n

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Q: 1. Show that the 2nd order difference equation (2) for 0²U 8² U 0x² ôt² = t> 0, U(x,0) = f(x),…

A: Given Show that the 2nd order difference equation (2) for   partial^ 2 U partial x ^ 2 = partial^ 2…

Q: Consider the differential equation x²dx-ydy=0 with the initial condition y(0) = 2. Approximate the…

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Q: 6. Simplify: 3+ 2i 3-21

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Q: by Consider the sequence of continuous functions {f} on [0, 1] given { nx 0<a<1/n 1/n ≤ x ≤ 1…

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Q: Express the surface integral 2x+3y+82-24. "11" xy²2 ds as an iterated double integral by using a…

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Q: Find the maximum for the profit function, P = 2x + 5y subject to the following constraints. 2x + y ≤…

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Q: Let A = 1 4 5 -1 -2 -3 and b = 6 28 34 O a=30 O a#-66 a=-66 a#70 a#30 [] a For what a, does the…

A: Given matrix A and b , we have to find for what value of a does the system of linear equation Ax = b…

Q: that Use the Alternating Series Estimation Theorem to find the smallest integer N so (-1)"+1 7n-1…

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Q: Use the graphs of f and g to evaluate g(f(2)) y 01 00 (-2,1) g (2,4) (2,-2) (4,3) X

A: We have to find out the value of g(f(2)) using the given graph.

Q: Let z = 5/² + 5/+ 17. Find the complex conjugate of z. The complex conjugate of z is Find the…

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Q: Exercise 8.3. In the schematic figures below, f: U → V is a linear transfor- mation. a. Draw f(au)…

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Q: Need help solving this USING MATHEMATICA (done in Mathematica using commands): Given a solid…

A: Answer : Mathematica code is    RegionPlot3D[ 0 &lt;= x &lt;= 4 - y^2 &amp;&amp; -2 &lt;= y &lt;= 2…

Q: 1001 0 111011 101100 010100 Suppose the above adjacency matrix identifies the network in a small…

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Q: Consider the following. f(x, y, z) = 9 z = 4 x XX 2 Lif E ZA (a) Express the triple integral z = 4+x…

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Q: 7. Find the Laurent series for f(z) = (cosh z cos z)/z³ that involves powers of z.

A: We have to find the laurent series of the function f(z).

Q: 6. For any positive integer n > 1 one has: (2n)! (n!)² n+1 <

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Q: Show that bessel functions satisfy |Jm(x)| ≤ 1 for m = 0, 1, 2...

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Q: Folve the IVP by a suitable substitution: dy dx - y-x x -, y(1) = 4

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Q: Find the solution of the linear differential equation (x³ - 3)y' + x²y = 3x²

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Q: Let a₁ = b= 4 []- [ a₂ = -3 a₁ + and b = Is b a linear combination of a₁ and a₂? OA. b is not a…

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Q: 0. 2 (1-7) ² n=1 any series test applied and show all work to justify your conclusion. Determine if…

A: Let,    We can find above series convegent or not by root test.

Q: An equation of a hyperbola is given. 36y² 25x² = 900 (a) Find the vertices, foci, and asymptotes of…

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Q: Evaluate 2-7i 3 +7i writing your answer in the form a + bi for real values of a and b. W = W

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Q: (b) Find Im (f) for f(z) = 22² + 3z +1 |z-1-2i|

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Q: The function f(x) = tan лx - 6 has a zero at (1/) arctan 6 ≈ 0.447431543 .Let Po = 0 and P₁ = 0.48…

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