1 Use the geometric series 1 Σ x* for |x| < 1, to find a power series representation k=0 for the following functions. 1 (a) f(x)= 1+x 1 (b) g(=) = 1 – x² (e) What are the radii of convergence of the power series above?

Q: Write the expression below in the form (a+ b) 1296x2 - 4320x°y + 5400xy 3000x'y + 625y

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Q: G8. Construct the graph where the vertices are you, your parents, and your grandparents with a…

A: Given : Vertices- you, parents and grand parents Relationship- born in same state.

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Q: G9. Draw a graph with 4 vertices each of degree 2.

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Q: dx 8y – x² – 12 dt - | dy - 2(x – 2)(y – 6) dt (a) Does there exist a yo > 0 such that if x(0) > 0…

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A: The differential equation of the form, dydx+py=Q is named as linear differential equation. The…

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Q: 1 j³ + 2 j=-0

A: Given that  ∑j=-∞∞1j3+1 consider the related integral ∑j=-∞∞1j3+1=∫Cdzz3+1 where the contour C. As…

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A: Here f is potential function of F .1st we will find f by using integration and then will use…

Q: 6. Find the volume generated by rotating the curve y = e-® about the x-axis on the interval [0, ∞)

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Q: frz,y)= 1²-2xy +y? (8,9, 1) Le t 27yty-z =0 Fea,y, z) = ² 21y+y-z

A: For the explanation follow the next step.

Q: Problem 1: Suppose that r (t) is a differentiable vector-valued function and the curve in the…

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Q: A function f(x) passes through the points (15.24). (18,37), and (22.25). Use the Lagrange Formula to…

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Q: A cake valued at $90 is divided among five players (P1, P2, P3, P4, P5) using the last diminisher…

A: Given: There are five players on the team, each with a cake value.At the end of round 1, their…

Q: s(s² + 4) - f(t) = ;(1 – sin 2t) . f(t) =(1 – cos 2t) C. f(t) = (1+ sin 2t) D. f(t) =(1+ cos 2t)

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Q: G6. Write down the adjacency list for the graph above:

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Q: 4" (x - 3)" (b) (-1)" Vn n=1

A: Given series is ∑n=1∞(-1)n4n(x-3)nn

Q: b) The region is between the curves y horizontal line y = 1. i, y = 1 and x = 0, above the x4 ,

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Q: Draw diagram to show the output of each phase of compiler for following expression. a +b-c*d

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Q: Let f(x)=x^3+x^2-3x-3 a) Find the location of the roots. b) Find an approximation for the positive…

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Q: Determine the present value P you must invest to have the future value A at simple interest rate r…

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Q: Q3. Find the inverse of the following matrix using inversion algorithm (using row/column operations)…

A: Given :  The given matrix is,   A = 31-121015-1 To find : We have to find the inverse of A  by using…

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A: Given : Number of science course= 4 Number of humanities courses =3 Number of Mathematics course=2

Q: Plot

A: Given, plot 78 and 88 on the number line.

Q: Find the value of x, y and z using Gaussian Elimination Method: ax + y + z = 1 x + ay + z = 1 x…

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Q: Use the compound interest formula to compute the total amount accumulated and the interest earned.…

A: Principal Amount P=$4,500 Time t =5 years Rate of interest r=1.7%=0.017 Compounded monthly n=12

Q: [MO22] Express as a single power series form: > (n – 2)an+1(2x – 3)*1 +) an-1(2x – 3)"-1 n=0 n=2

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Q: Use the compound interest formula to compute the total amount accumulated and the interest earned.…

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Q: The radius of convergence for the series En=1 n2(x+2)" is 2n 2 1 O

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Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

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Q: 0.5 coS X dxp. Using the Riemann sum (at the midpoints) with n=8, approximate the value of the…

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Q: If z/w = 6 - j8 when z = 22 + j4, what is the argument of w?

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Q: 5s s+4 s2 + 16 -f(t) 3e 4t-5 cos 4t C. f(t) = 3e¬t - 5 sin 4t .f(t) = 3et-5 cos 4t D. f(t) = 3et - 5…

A: Given Laplace transform is F(s) = 3s + 4 - 5ss2 + 16

Q: G14. Draw two 'different' graphs with five vertices and degrees {1, 2, 2, 2, 3).

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Q: x"(t)– 3x'(t)– y' (f)+ 2 y(t)= 14t + 3 x'(t)– 3x(t)+ y'(1)= 1 x (0) = 0 x'(0) =0 y (0) = 6.5 -…

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

Q: Proof of CRT ( for two moduli) We must proue that f: Zm,m Zmx Zm given by m,) is a bijecdion.

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Q: You are given a choice of taking the simple interest on $100,000 invested for 3 years at a rate of…

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Q: Solve by theorems of linearity and translation. f(t) = cos t + sin t

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Q: G5: What is the degree of vertex 2? Degree =

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