Verify the divergence theorem for F= (xy+y2²)i+x²yj and the volume V in the first octant bounded by x = 0, y = 0, z = 0, z = 1 and x² + y² = 4.

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A: Given: z=2cis3π4 To find: Rectangular form of given complex number.

Q: 5. A = {0, 32, 62} where A-Z* 6. A = [5, 10-] where A = Z¹

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Q: 1 1. H = Span Suppose : = The projection of von H is: [1] 0 {Q.A]} 1

A: Given, ν→=111 H is the vector spanned by 011and 101.

Q: If A is an orthogonal matrix, then det(A) = ±1.

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Q: 8. Sketch the roots of 28 =-16

A: This is a problem of complex analysis.

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Q: For this problem, let f(x) = e. i Find the curvature of f(x). Sketch f and its curvature function.…

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Q: Solve the following equation x²+3x+2-i = 0

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Q: 1. The Set of polynomials of degree ≤ 5 is a vector space. a. True b. False 2. If S = {a, b, c...,…

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Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x- 2ky + 5z = 0…

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Q: Advanced Math proof? Theorem 7.3. Let T be a linear operator on a finite-dimensional vector space V…

A: We prove this theorem by using contradiction on Si for some i= 1,2,3,....,k.

Q: Solve the given homogeneous ODE. (Also. state the value of a. x² + y² + (x² − xy) dy = 0 a = =

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Q: 1. V=R³ S = {12 :* ER}. 3x Let V be a vector space and S be a subset of V. Determine whether S is a…

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Q: Use power series to solve the following differential equations: (a) 3y" + xy + 4y = 0 (x = 0 is…

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Q: Show that the given conditional statement (p ^q) v(p ^r) → (q vr) is a tautology using truth table.

A: We know that ,  Conditional Statement are those Statement where a hypothesis is followed by a…

Q: Consider minimizing the above objective fuction for the following numerical example: A = 0.5, y = 1,…

A: Given: λ=0.5, y=1, x=10 To find: Solution

Q: Domain: Range:

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Q: Identify whether the following graph is Eulerian or Hamiltonian. And Why ? 1. 2. 3.

A: As per our guidelines we are supposed to answer first three parts.    Theorem : A connected graph is…

Q: Euler circuit and a Hamilton circuit. Come up with and post two real world problems that require…

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Q: ). y" + y = sec t, 0<t</2; y = (cos t) In cos t+tsin t

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Q: Evaluate ff, F.dS, where F= (4xz, -y², yz) and Sis the surface of the cube bounded by the planes x =…

A: We will use divergence theorem to find given integral  ∫∫SF→dS →= ∫∫∫EdivF→ dV Where E is  solid…

Q: 8 7 6 54 32 3 1 -4-3-2-1 + valuate f(2): (2) = olve f(x) = 2: 1 2 3 4 5

A: since horizontal axis represent x values and vertical axis represent f(x) values. so, from graph we…

Q: Using the transformation x+y=u, = V show that ["dy [~ #²e²" dx = ["du ["e du = e²-1 x+ye 0 0

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Q: If F = yi + (x - 2xz)j - xyk, evaluate the surface integral ff, (curl F) dS, where S is the surface…

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Q: 9.7 Solve fooring Functions 356 2x a) 2 256 x 4 b) 16 = 4+2=3 64 C) log * = 4 = जानिर Dibuponi sulol

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Q: Emily is making a closed rectangular box with a square base from two different woods. The wood for…

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Q: CLAMPED SPLINE MODEL PROBLEM = Suppose S(x) interpolates f(x) atxo = 0, x₁ 1 and 2 = 2 by a clamped…

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Q: 14a) 14b) f(x)= 2 4x-15 about the center x = 4 f(x) = ln(1+5x¹) about the center x = 0

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Q: 1. Bees are constantly moving in and out of two bee hives, A and B. The rate of change in the number…

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Q: Determine if the given function is a linear transformation. 0 0 1 T: M3,3 → M3,3) T(A) = 0 10 A

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Q: Consider the differential equation: dy dt y² +4y³-12y² a) What are the equilibra? b) On what…

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Q: If the rational function graphed below appears to approach a vertical or horizontal line, then…

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Q: What is the value of 86 0 -9 -350 6 5-80 1 5 11 0 -9 A. 129 B. 235 C. 0 D. 1 E. None of the above…

A: We find the value of given determinant

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Q: The 0, -1), B(-4, -1, 0), and C(3, 1, 1), find: following are the vertices of a triangle A(4,

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Q: Let Ω-set of all real numbers, A-index set. Identify the generalized union and intersection of the…

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Q: 9.6 function by Using TMR enoits aut Graph Following J- Co (x+2)

A: Given: y=cosx+90° To find: Graphical representation.

Q: Suppose that at each birth, having a girl is not as likely as having a boy. The probability…

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Q: Lagrange Interpolating Polynomial Problem Suppose that the Lagrange polynomial passes through the…

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: b. Evaluate g (4). Enter the exact answer. g (4) = Number c. What is the minimum distance between…

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