5. Show that the function h(x, y) defined by 1 if a? + y? < 1 1-x²-y² h(x, y) = 0; if r? + y? > 1 is discontinuous.

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A: For the solution of the problem follow the next step.

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Q: 3. Show that the Fourier series of the function g(x) = |x| on the interval [-7,7] is 4 5 - 1 cos(2n…

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Q: 4. Let F(n) = 2F(n – 1) + 5F(n – 2) – 6F(n – 3) with initial conditions F(0) = 4, F(1) = -4 and F(2)…

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Q: 8. (The argument principle and Rouché's theorem) (a) Determine the number of zeros in the right…

A: (a) The given function is pz=z3+z2+9z+4 let's consider Pz=hz+qz such that hz=z2+9z+4 and qz=z3…

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A: Given f(x) = x,0≤x&lt;11,x≥1

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Q: pheroidal coordina h1

A: Laplacian: ∇2=1h1h2h3∂∂ηh2h3h1∂∂η+∂∂θh1h3h2∂∂θ+∂∂ϕh1h2h3∂∂ϕ Given:…

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Q: (b) 3r+1 = 52

A: Q (b) asked and answered.

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Q: Express the given Cartesian complex numbers in polar form. A. 2+J3 b. -4 c. -6+J

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Q: Problem 8: In electromagnetic scattering by an infinite cylinder of radius a, under certain…

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Q: 5.A franchisee knows that his labor cost to net sales ratio is 2 to 3. If this estimated labor cost…

A: This problem is a simple application of ratio and I solved it in the next step.

Q: Question 1 In a sequence there can be repeated elements. O True False

A: We have to say a sequence have repeated elements or not.

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: 16. Given the differential equation and the solution. determine the wronskian -3+2y 0 dx2 ex %3D y =…

A: Given differential equation is d2ydx2 - 3dydx + 2y = 0 with solution y = Aex + Be2x

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Q: Question: H.W F(X)={ 2-4 Find Odd And Even Function (Half Range) Fourier Series Of Function Below…

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Q: y' = 5xy-2x

A: Find the general solution of the given differential equation using separation of variables :-

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Q: 4. Prove or disprove. Given n (n > 1) evenis A. A A, E, then EPIA)-E PIA, n4) s PIU41 = PIAI P[4]…

A: Given: n&gt;1 events, A1,A2,...,An∈ζ.   To prove or disprove:…

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: (b) Find the powers series expansion around z = 0 for the function 1/(2² – 5z + 6) and determine its…

A: As we need power series expansion about z=0 so here we can use sum of infinite GP ( geometric…

Q: Solve the following recurrence relations. 4an-2,n > 2; ao 0 and aj = = 4. a) an b) а, 3D 2ад-1+…

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Q: Interpreting a Linear Equation At 12:00 P.M. the volume of water in a tank started changing steadily…

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Q: A, BE R"Xn 2. Let n EN. Consider the following binary relation for A-B : 3Q E R"*": Q. A A= QB…

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Q: Find the volume of the se

A: Given, the curve                   y2(a+x)=x2(a-x)

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A: Since you have posted a multiple question according to guildlines I will solve first question for…

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Q: Evaluate the indefinite integral as a power series. x6 In(1 + x) dx f(x) = C + > x „6 (-1)"-x"+1 n+1…

A: The logarithm series formula states that ln1+x=∑n=0∞-1nxn+1n+1, x&lt;1. Substitute ∑n=0∞-1nxn+1n+1…

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Q: a) 2x " + 2x'+ x = 3 cos 10t answer: (-597/4001)cos(10t) + (60/4001)sin(10t), i need to know how to…

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Q: 4s+4 Find the inverse transform: F(s) %3D s2 (s-2)

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Q: Solve the following recurrence relations. 4an-2,n > 2; ao 0 and aj = = 4. a) an b) а, 3D 2ад-1+…

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A: Solution : Given that  General exponential equation    y = y0 ekt   ---(1)

Q: Given (xi , xi2022 i ) ∀i = 0, ..., n, where x0 = −1, x1 = 0, x2 = 1, x3 = 2, ..., xn = n − 1. Write…

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Q: fa) a z n-> (2-4)스

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Q: 3. (Laurent series expansions) Find the Laurent series expansions of the following functions in the…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: R is the region bounded by the given curves. R: y = x², x = 0, x = 1, x-axis Find I, Ry, Iyı R.…

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Q: 2х — 8y + 5z 3D-5 2х + у —z%3D12 — 5х + 3у + 9z 3-17

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Q: Continuity 4. Let f(r,y) be a function defined on a disk D mot containing the origin which is given…

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Q: The general solution of x*y = -x³y- csc(xy) is A 2x?сos(xy) - 1 %3D сх B 2x²cos(xy) +1= cx² c)…

A: We have given a differential equation ,  x4y' = - x3y - csc(xy) x4dydx = -x3y - csc(xy) Here , plug…

Q: Given: A = 0.6 – j0.4 B = 0.5 + j0.8 C = 0.6 – j0.8 D = 0.5 + j0.4 Evaluate: (c+)/ log. (3B) (cos…

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