Use contour integrals and Cauchy Residue Theorem to calculate the following integral Justify your answer.

Q: Gil rolls a number cube 78 times.  How many times can he expect to roll an odd number greater than…

A: Assuming its just a regular number cube with 6 numbers, there are only 2 odd numbers above 1 ( 3…

Q: -2 -1 2 -5 1 -1 -2 canonical form, and determine JCF(A). Let A Find an invertible matrix S such that…

A: From the given matrix A we find the characteristics equation and solving we get eigen values.

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Q: Given the eigenvalues: λ = -5 and -2, find an invertible matrix P and a diagonal matrix Q for the…

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Q: Find the minimum value of f(₁84)x₁+28+ Ay subject to the following constraints. Write the exact…

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Q: Determine whether the following subset of P2 is a subspace of P2. {p(1): S p(t)dt :=0} Note: Pn is…

A: Let,      S = { p(t) : 0∫1 p(t)dt = 0 }    Then, clearly, S is a subset of P2  [set of all…

Q: Find the null space of the following matrix A, i.e. find the subspace of all a basis of this null…

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Q: Consider the following: IM Using a as the root of the tree and a depth-first search, which graph…

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Q: 3. For each linear operator T on V, find the minimal polynomial of T. (c) V = P2(R) and T( (x)) = -x…

A: Linear algebra

Q: Solve x + 1 > 4, x + 11 > 14, x + 21 > 24. Complete the description of a pattern. Then use the…

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Q: 3y 3x √√x² + y² √√x² + y² assortment of points on the circle x² + y² = 25. Draw the spin field F = j…

A: Given vector field is: F=-3yx2+y2i+3xx2+y2j. Given circle is: x2+y2=25. Substitute in the given…

Q: Considet the quadratic integer ring Z[sqrt{D}] where D is a square free integer (a) Show 3 is…

A: Given , ℤD  is a ring . (a).  3 is reducible in  D=-2 yet irreducible in  D=-5 . (b).  Is 3 is prime…

Q: Let I and J be ideals of a ring R.Prove that I+J= , the ideal of R generated by I ∪ J.

A: I and J are the ideals of a ring R.

Q: solve the given ODE y'''-4y"-y'+4y=30e^2x

A: Given given y111-4y11-y1+4y=30e2x   ⇒d3ydx3-4d2ydx2-dydx+4y=30e2xLet ddx=D so that…

Q: Let C be the circle |z| = 3 described in the positive sense and 22²-2-2 |w| 3. g(w) = √ 2 3² C…

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Q: e)z = √√9-x² - y² 1 f)f(x,y) = √₁-x²-y²² onde x² + y² ≤1

A: A function: a) z=9-x2-y2 b) fx , y=11-x2-y2 on  x2+y2≤1 To Find: Contour line and their graph.

Q: Find a set of orthonormal vectors that span the same space as the set below: 8 X1 = 2X2 = , X3 =

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Q: ) The linear transformation T(x1, x2, x3, x4) = (x₁ - x₂ + x3 T is given by the following formula…

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Q: An executive has to visit 1 of his 5 plants for an inspection. If these plants are numbered 1, 2, 3,…

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Q: Instructions: Please Do not use the matrix methods. Please show your calculations step by step on…

A: The equation of the line is given as       (x - 4)/2 = y/1 = (z + 1)/(-1)    Then, for any point on…

Q: Find a basis of the following subspace of R³: W linear independence. {(a+b,b+c, c-a)}. Hint:…

A: Given Subspace is, W={(a+b,b+c,c-a):a,b,c∈ℝ}   Now, (a+b,b+c,c-a) =a(1,0,-1)+b(1,1,0)+c(0,1,1)   So,…

Q: Use contour integrals and Cauchy Residue Theorem to calculate the following integral Justify your…

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Q: 1.Let’s consider: U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, V = {0, 2, 4, 6, 8}, D = {1, 3, 5, 7, 9}, P =…

A: Here given that    U={0,1,2,3,4,5,6,7,8,9}V={0,2,4,6,8}D={1,3,5,7,9}P={2,3,5,7} That means V is set…

Q: find the solution of the given initial value problem, and plot its graph. How does the solution…

A: Since the given initial value at t=0 so we can apply Laplace Transformation for solving this ode.

Q: 7. Let Þ(u, v) = (6u — 4v, u +3v). Use the Jacobian determinant to determine the area of Þ(S) where…

A: The formula is S*jacobian of phi

Q: Let FCR denote the field of constructible numbers. Prove that there is no injective group…

A: Let F ⊂ R denote the field of constructible numbers. We have to prove that there is no injective…

Q: Let x, y = {0, 1}" and let s = xy. Show 1 Hon • (2x) + √2)=√√ Σ (-1)ײ |z) z={s}+ 2n-

A: The Hadamard transform is a quantum gate that is commonly used in quantum algorithms and circuits.…

Q: Using a direct proof, prove that Fn+1 3Fn-3 +5F-1 +2F-5, for any Fibonacci number when n ≥ 6.

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Q: True or False? Upload your reasoning. If the statement is true give a proof or detailed reason why…

A: We know that If W is a non-empty subset of a vector space  (linear space) V , then W is a subspace…

Q: Find the rank and nullity of the T(ƒ(t)) = t(ƒ'(t)) from P₂ to P₂ transformation T.

A: Given the transformation  T  from  P2 to P2 i.e.   T : P2 → P2 given by ,            T(f(t)) =…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Use contour integrals and Cauchy Residue Theorem to calculate the following integral Justify your…

A: h) To evaluate the integral  ∫₀^∞ 1/((x + 1)(x² + 2x + 5)) dx, we will use the method of contour…

Q: The figure here shows the vector field Vf, where f is con- tinuously differentiable in the whole…

A: From the plot of the vector field ∇f, it is clear that ∇f is constant for all points in the domain…

Q: Does the vector t belong to the Span(u,v,w)? Support your answer with calculation. (a) u = (1,3,2),…

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Q: 968 CHAPTER 14 Partial Derivatives A MON 4. f(x, y) = 3x -x³-2y² + y4 5-20 Find the local maximum…

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Q: L[(1 et + 3e-4t) cos 5t] = Find cm - b + na S s²b (s+a) - b mns +

A: Solution: Given  that  ℒ{(1-et+3e-4t)cos(5t)}=ss2-b+(m-ns)(s+a)c-b………(1)Let  f(t)=1-et+3e-4tNow,…

Q: A space probe in the shape of the ellipsoid 16x² + y² +42² = 41 enters a planet's atmosphere and its…

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Q: d. (x,y,z]-[-2,1,3]+s[3,-1,-7] And d, [x,y,z]=[2,2,2]+[2.-1,-1]

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Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…

Q: What is the tangent line approximation to e near x = 6? NOTE: Enter your formula exactly, or round…

A: We have to find tangent line approximation to ex near x=6

Q: Find the Laplace transform of the following function. f(t) = t Slev 0 (e sin (4(t-v)) dv

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Q: Let E ⊂ ℝ and y ∈ ℝ. Show that E is measurable iff E + y := {x + y : x ∈ E} is measurable. Give a…

A: E⊂ℝ, y⊂ℝ

Q: 2) [Solve by hand-writing] Find the root of the following nonlinear problem using the iterative…

A: Let us find the root of  f(x)=0 by Newton Raphson method:  Step-1: Finding f'(x)  Note that the…

Q: Let Consider the complex inner product space C³ with the usual inner product (u, v) = ₁V₁ + U₂ V₂ +…

A: Inner products space

Q: By means of elementary row operations, find an invertible 3 × 3 matrix R such that RA= B where a+a…

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Q: Using u = x the ODE dy dx = y²ex/y x²-2xy becomes

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Q: . The solid E, shown below, is the region enclosed by x + z² = 1, x = 0, y = 0, y = 2, and z = 0.…

A: Given that  the solid E is bounded in the region enclosed by  x + z2 = 1 ,  x = 0 ,  y = 0 ,…

Q: Find the area of the region. three petals of  r = cos(9?)

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Q: 13. f(x, y, z, t) = x+y+z+t; x² + y² + z² + 1² = 1

A: The given function is, f(x,y,z,t)=x+y+z+tx2+y2+z2+t2=1 The Lagrange multiplier concept is: The…

Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

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