. Use mathematical induction to show that n Σ r=1 (2r − 1)² = 1² + 3² +5² + + (2n − 1)² = = n(2n − 1) (2n + 1) 3

Q: 2. Suppose f, g € F[x]. Prove that GalƑ(fg) ≈ H, where H < GalƑ (f) × GalƑ(g). You may assume F is a…

A: Now,

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A: A matrix A=11101011 ,b=-1216 To Find: The least square solution of the system Ax=b

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Q: Let xit) and y(t) be c functions on R and let zt=xt . Let A be a 2x2 real constant matrix such that…

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Q: Q47. If I = √√√1 + cos x dx, then the domain of I is?

A: First we integrate and then find the domain of I

Q: TABLE 13-2 $ Period 2% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 40 50 4% 5% 7% 9%…

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Q: 23, 24, 25 and 26 Find a power series representation for f, and graph f and several partial sums sn…

A: The power series of a function can be obtained by finding Taylor's polynomial. Taylor's polynomial…

Q: (a). (n+2)! n! (b). 12C4

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Q: Question 10 Consider the following curves: x = 3 + cost x = 3 sint A = x = 12 cost y = 9 sin t t =…

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Q: Which of the following statements are true? 1) Something else not listed here 02)√²9=x-3 03) = 0 0…

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Q: Find E3,3 using the law according to the mittag Leffler function Γ(β)zn Σr(a(n-1) + B) Eaß(z) = z +…

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Q: The equation log10 (2x-3) = 0 has solution: 0₁)=4 2) None of the choices here are correct 032=2 042…

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Q: Find the length of the hypotenuse of a right triangle whose catheters measure 9 and 12 centimeters.

A: The Pythagorean theorem is a theorem which states that the square of the hypotenuse is equal to the…

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Q: Use the Binomial Theorem to complete the expansion of (r-s)3.

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Q: $ TABLE 13-3 Sinking fund table based on $1 Required amount Frequency of payment 24,100 Quarterly…

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Q: 1. Here are two cool lines: ₁ has parametric equations x = 6 +4t, x+1 l₂ has the symmetric equation…

A: 1) a)The given  equation  of the  lines  are l1 : x=(6+4t),y=(4-3t),z=(-7+t)…

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Q: 67. / 1 ex e xp

A: ∫01exx2dx To Find: Use comparision test to determine whether or not the integral converges.

Q: 1. lim X45 3x²+7x-7 x² +9 A. 3 B. C. 3 D. undefined 14 = is: 10

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Q: O classify the following PDEs :- 22 Z 82 2 <-2 +2 =x+3y албу 2 X • x Ихх - 2ху Иху ну иду • дго дуг…

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Q: Which test(s) could be used to determine if the series in converges or diverges? Select all that…

A: As 0wr the question we are given an infinite series and we have to check which one of the following…

Q: Solve the IBVP below and express your final answer without using series notation. Ut = Uxx + cos(2t)…

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Q: 9. 10. 1. f(t) = cos(bt) f(t) = eat sin(bt) f(t) = eat cos(bt)

A: We will find the Laplace transformation for the given functions :  9) ft=cosbt 11)  ft=eatcosbt

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A: Given y1=y-x,y(0)=2, h=0.1By fouth-order Runge Kutta method y1=y0+16k1+2k2+2k3+k4

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Q: Write and solve the Euler equations to make the following integrals stationary

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Q: 3. Find the singular value representation of the matrix 2 2 - (-²²). A =

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Q: using direct proofs: proof that, if x is an odd integer, then x+5 is even

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Q: (a) Show that P is a vector space over R.

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Q: 3. Cortes Highschool has the following growth of enrolment" Enrolment Year Enrolment 2019 3,000 2020…

A: We will use least square regression method since it's one type of trend projection method.

Q: Find E3,1 using the law according to the mittag Leffler function Γ(β)z" r(a(n-1) + B) Ea,ß(z) = z +…

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Q: Solve the following ODE: x²y" - 5xy' +10y = 0 y(1)= a, y'(1) = b

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