Find the radius of convergence of the following series. (3k)!xk Σ k=1 (k!)³ The radius of convergence is R= (Simplify your answer.)

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A: Given: A=1110   To find: Eigen values and orthonormal eigen vectors of ATA and AAT. To find: The…

Q: ди Ət 22 u дх2, 0 0 ди ди ən (0, t) = ôå (2, t) = 0, t > 0 = u(x, 0) = 2 — 4x, 0 < x < 2

A: Given heat equation is ∂u∂t=∂2u∂x2,    0&lt;x&lt;2, t&gt;0            (1)∂u∂x0,t=∂u∂x2,t=0,…

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Q: Exercise 1. Calculate the flow of induced by the field f: (-∞, 1) × (-∞, 1)→ R given by X f(t, x) =…

A: As per the question we are given a field f in tx-plane defined by : f(t, x) = 1/√((1-t)(1-x))  ,…

Q: 11) Example: of R' (t) to find the curvature Use the Theorem in 10 to

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Q: Decide which of the rational functions might have the given graph. O R(x) = OR(X)= O R(x) = O 2 -1…

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Q: = Express by ¡y¡ in the terms of x variables where y; = C₁jx; and bicik = 8%.

A: express bijyiyj in the terms of x variables where yi=cijxj             ...i and bijcik=δik…

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Q: Calculate the following triple integrals: 1 S S Sr (z+y+:+1)² dædydz, where T is the region bounded…

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Q: 4. Using Principal Component Analysis, reduce the dimensionality 2 1 3 4 5 0 7 6 Data = L9 2-

A: New data set

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A: To Match each series series with either Convergent "C" or Divergent "D".   1. ∑n=2∞ 5n10-81 2. ∑n=1∞…

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Q: 16) The series Σ(-1)+1 76mm 1 a) True b) False converges conditionally. 17) de converges if and only…

A: Solution 16: Given series is ∑n=1∞(-1)n+1arctan(n)n2 Let an=arctan(n)n2 Here an+1≤an and limn→∞an=0…

Q: -t С. У +2y + y = 6te у (O) =ЎCo) =0

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Q: Q3: the - Using inverse Convolution Theorom, find Fourier transform of that 6+52w-w²1 given £-'f…

A: Introduction: Like Laplace transformation, convolution theorem is also used Fourier transformation.…

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A: We need to find the probability that neither marble is yellow. Given  Yellow = 4 Green = 3 Red = 3

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Q: How is the area y > -1 converted by mapping w = iz ?

A: Given area y&gt;-1 mapping is w=iz Let w=u+ivz=x+iv

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Q: (d) (i) (ii) Convert 54° to radians, leaving your answer in terms of . Use your answer from part (d)…

A: Area of the sector

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Q: Use logarithmic differentiation to find the derivative of the function y=(x²+3)² (2x³-5) 27

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Q: Find the area of the following region. The region common to the circles r= -6 sin 0 and r= 3. The…

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Q: 12) Prove Ñ' (t) are Smooth space for any always orthogonal (*+Edom R³). that Curve R(t), 7(t) and

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Q: H.w2: Use Runge-Kutta Method with (h = 0.1) to solve the eqaution y" + 3xy' -6y=0 with y (0) = 1,…

A: It is provided that y''+3xy'-6y=0, y(o=1, y'(0.1)=0.1. We need to calculate y(0.5), y'(0.1) using…

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Q: DO ) Find the interval of convergence where the power series Σ k=3 k² (3x −4)* - 2k+1 converges.

A: This is a problem of power series where we are to apply radius of convergence formula for power…

Q: A solid of constant density is bounded below by the plane z = 0, above by the cone z = r, r ≥ 0, and…

A: Consider a solid of constant density is bounded below by the planez=0, above by the conez=r, r≥0,…

Q: (c) Show that Green's Theorem is satisfied by evaluating both the line integral and the double…

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Q: Consider the geometric series 1-tan²0+ tan¹0 - (i) When the limiting sum exists, find its value in…

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Q: D Question 18 Differentiate. y = (9x+5)*

A: 18. To differentiate: y=9x+5x

Q: PROBLEMS 3.2 Find the x-and y-components of each vector in the following diagram. (Express them as…

A: As per company guidelines we are allowed to solve one question at a time and maximum three sub-parts…

Q: Two parabolas are given: - C₁ is the curve of intersection between y = 1-2² and 2 = - C₂ is the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: We fit a model V = aPb to the data below using the least squares criterion. Vi 2.27 2.4 3.31 3.27…

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Q: Find the value of x 16x³-24x²+44x-24 = 0

A: Solution :- Given equation :- 16x3-24x2+44x-24=0Since , it is complex polynomial , we will use…

Q: EX: Solve the ед. Ў+зу +2fy ht=zuct-)) , усо) =1

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Q: 1 Find the value of the integral 1₂ Determine whether the series ∞ dx 2 9x (ln(3x))² n=2 1 9n…

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Q: jw F(w). jw F(W) = jw F(W) = [ [2 - acos (WT) 2 - A Трия cos -2A (₁-COS (NT)) Тјия - 2A (asin ²…

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Q: Find the complex Fourier series coefficients for the signal x(t)= (sin(nwot))5

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Q: please provide an explanation and rationale to show) its unique critical point, 2) point is not a…

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Q: Find the interval of convergence for the power series 1(-1)" O [-5,1] O (-5,1] O (-1,5] O [-1,5) O…

A: To find interval of convergence we use Root test.

Q: Use a suitable change of variables to determine the indefinite integral 1 dx Love + 2x +x

A: Substitute1+x2=t.

Q: (c) Figure 6 shows the triangle ABC, with all side lengths measured in centimetres. 10.3 cm 16.5 cm…

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Q: Find the new equation of the final image given below. A circle with equation x² + y² - 2x - 4y = 4…

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Q: Question 10 Calculate the standard deviation and variance of the sample data shown, to two decimal…

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