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Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: so if…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: Q2 Let B = {1,2,3, ..., 1240}. Prove that in any subset of 621 elements of B, there are two elements…

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Q: 30. Let S= {1,2,3} and let R be an equivalence relation on S. (a) Describe the R with the fewest…

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Q: Question Two Solve For x in the following i. 2x+3 21-x + 15 %3D ii. log (6x + 4) – log (x – 6) = 1…

A: As per the company guidelines, we are supposed to answer only first 3 subparts in case of multipart…

Q: If K is a normal subgroup of a finite group G and S is a Sylow p-suby

A: Given that if K is a normal subgroup of a finite group  G and S is a Sylow p-subgroup of G. then K∩S…

Q: 1. Consider the following operations on Z a) m*n = m2 + n? b) m*n (m+n)/2 Prove or disprove: 1. a)…

A: Let us prove or disprove the properties 1- 4 in the next steps.

Q: (b) List all the subgroups of Z, including the "obvious" or "trivial" ones. Explain how you…

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Q: 2. Find the MacLaurin series and its radius of convergence for the function sin(z²) Show the details…

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Q: Show that any 2-cut relation (for > 0) of a fuzzy equivalence relation results in a crisp…

A: Let's take the fuzzy relation: R = 10.800.10.20.810.400.900.41000.10010.50.20.900.51 Fuzzy tolerance…

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

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Q: Using initial estimates for the solution to be {0.0.0}, what is the solution to the system 5x, - 2x,…

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Q: iven by 5x3 at x = 1 is: %3D

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Q: 1. Which of the following is an integral representation of the gamma function? dx r(x) = x - 1)1 dx…

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Q: To solve the equation 2 sin x = x by Newton- Raphson method, the initial guess was chosen to be x =…

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Q: Determine the estimate for the value of z in the system *+20y+ z -18 25x +y-5z= 19 3 +4y + 8z =7…

A: The given problem is find the solution for z for the given system of linear equations using Gauss…

Q: Consider the function f(x) = cos(2x). %3D 1. Find the Taylor series for f(x) at x = T.

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Q: (a) Show that the series g(3) = E( 1 Z- NA z+ nA n=1 for every z # ma for any nonzero integer m and…

A: To Show- Show that the series gz = ∑n=1∞1z - nπ + 1z + nπ converges for every z ≠ mπ for any nonzero…

Q: Use the Integral Test to determine whether the infinite series is convergent. Σ -- n n=1 Fill in the…

A: Given series is ∑n=1∞n-9

Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) 36 c) V11²510716 State…

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Q: Given that S' = {e® : 0 € R}, where e" = cos(0) + i sin(0). %3D Show that S' is a group under…

A: Introduction: A group is an algebraic structure. The algebraic structure is an ordered pair that…

Q: Calculate the indicated Riemann sum S, for the function f(x) = x - 9x - 22. Partition [0,6] into…

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Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

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Q: 2. Prove that a. lim, b. lim,1

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Q: Bre anna had a ba sket she de cided to give appler plus 1 to her Father, OF apples . aw ay 2 her OF…

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Q: - the region 1, x = 0, y = %3D

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Q: If u = tan- the value of x2 +y? +xy du du at x = 1 and y = 3 is

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Q: 4) In how many ways you express 10$ as a sum of dimes (10c) and quarters (0.25$)? 5) Solve 50000a +…

A: To solve this problem we use the concept of diophantine   equation .  Diophantine equation : An…

Q: x In x at 0 < x < 1 1-x Show that the function f () at x = 0 is integrable on the interval 0, 1]. -1…

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Q: EX' 1) show That. the ring of Complex numbers can be imbed iny in ariny 2x 2 matreces.(M 241

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Q: A is closed if and only A-A

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Q: (b) List all the subgroups of Z, including the "obvious" or "trivial" ones. Explain how you…

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Q: Let S be the spanning tree of any graph. Prove that if we add any edge to S to unchanged set of…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Euler methed to solve use ycoleo

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Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: Sx + 1…

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Q: Create two 2 x 2 matrices A and B, to show that (A+ B) - A+B is not always true. Clearly write A, B,…

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Q: 12 -9 X' 4

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Q: What is needed algebraically and calculus-wise to find relative and absolute extrema? What does it…

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Q: confirm that the intergal test is applicable and use in to determine whether the series converges…

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Q: (d) Prove Ker(f) = 1/J (e) Apply the Fundamental Homomorphism Theorem (FHT)

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Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

Q: Consider A = (0, 4, 2) , B =, (6, –1, 0) and C = (3,0, 1) %3D 1 (a) Find the unit vector having the…

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Q: The temperature (T) at which water bols. varies inversely as the number of feet (h) above sea level.…

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Q: State the value(s) of k such that the following system of linear Cquations has infinitely many…

A: The given system of linear equations…

Q: P) use a power Series to approslnete tue Value of the integral 4 e doc with en e mor of less fren…

A: We will use power series of ex ex=∑n=0∞xnn! Let   ∑n=0∞anbe a series satisfying all of the…

Q: Find a formula in terms of k for the entries of A", where A is the diagonalizable matrix below, and…

A: If A is a diagonalizable matrix, then there exists a invertible matrix P and a diagonal matrix D…

Q: 1. Given the function f(x) = () (a) Find a power-series representation for f(x). | f(x) da = n(n +1)…

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Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B × A). C,…

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Q: Suppose g is a primitive root mod p (with p an odd prime) such that g +1 mod p? Prove g must be a…

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Q: Given: In(1+ x) = > (-1)" -xn+1 if |x| < 1 n + 1 n=0 Use the third degree Maclaurin polynomial of f…

A: Third degree polynomial to approximate f

Q: Find the centroid of the region bounded by the graphs of 343 y = x, x = and y = 14. y? * NOTE: Enter…

A: We have to find centroid of given bounded region.