Proof that Cauchy's and D'Alamberts criterium gives same result. (Infinity series)

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Q: Find f[g(x)] and g[f(x)] for the given functions. 10 f(x) = g(x)=x² X f[g(x)] =

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Q: ). Express the volume of the region in the first octant, bounded by the cylinder x² + y² = 1, below…

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Q: -8 15

A: This is a question of Linear transformation.

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Q: If the 9 by 12 system Ax = b is solvable for every b, then C(A) = __ .

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Q: Question 4 Given the differential equation: dy dx + 2xy=x²-1 Which of the following substitution is…

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Q: re Question 9 O The position of an object is described by x(t) O Ⓒz(t) = 2 (e-³-e-M) z(t)= O z(t) =…

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A: Given: A=0-5231-3-4-43 To find : Vector x and y with  xs=1  and  ym=1 such that A1=Axs    and…

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Q: 12. Let C be the curve of the intersection of the cylinder x² + y² = 4 and the plane x+y+z= 1.…

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Q: Find the volume of the region bounded by x² + 3y² = z and y² + z = 4.

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Q: Particular solution by inspection Solve the following equation: y^(7)+4y^(5)+4y^(3)=120

A: Kindly refer to Step 2 for the solution.

Q: Ly A Click Submit to complete this assessment. Question 10 Given a differential equation with…

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Q: Compute the following: a. (2+5)* b. (4-3i)¹/6 c. Simplify: cos 50+isin50 cos 40+isin40 d. If z = cos…

A: De Moivre's theorem:-  (Cosθ + i Sinθ)n= Cos nθ + i Sin nθ where n is rational number.   Exponential…

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Q: 2x + 3y + 3z = 2 4x – 3y – 6z = 2 10x – 6y + 3z = 0 Given values – 144, -192, and 96 for Dx, Dy,…

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Q: 3 • / (√x ² − 21 2² cos(3³) dx + ( xy² + x² + x³y² sin(y)) dy where C is the boundary of the region…

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Q: Show that if f: R→ R is continuous and f(x) = 0 for every rational number a, men f(x)= 0 for all z.

A: Thank you for the question. According to our guidelines we can answer only  first question and…

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Q: 4s-1 c. F(s)=²+5s +6 2 e. F(s) = 3s-1 1.4s²4.48s +2.94 d. f. 2s+5 S s² +1.2s+.2924 F(s)=- F(s) = 3s…

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Q: At a pottery factory, fuel consumption for heating the kilns varies with the size of the order being…

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Q: 9. (D²+1)y = cotx 10. y" - 2y' + y == ex x²+1

A: By the method of variation of parameters

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Q: Question 11 For f(x, y) = x¹y+y+ 2², calculate f. (2, 1). O O 20 10 40 80

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Q: 7. 6y" - 12y' + 6y = x

A: The problems 6,7,8 are individual problems so I solve one problem only.

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Q: Calculate the gradient ∇f, where f(x, y) = ln(x2 + y2) (here (x, y) ̸= (0, 0)).

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Q: Use the law of sines, the law of cosines, or the Pythagorean Theorem to solve ∆ABC. Round to one…

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