B. FOURIER SERIES OF PERIODIC FUNCTIONS 3. Interval – 1

Q: 2. Show that p q is congruent to (p - 4)A .

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A: As per policy, we are allowed to answer only one question at a time. So, I am answering the first…

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Q: Can you make an xy table and graph out of this

A: The xy table and graph of the given function are as shown below.

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: Q;: A. Let G be a group. Show that G is abelain iff the mapping f:G→G defined by f(x)=x", VxeG is an…

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Q: Arrow's Impossibility Theorem implies that there is a voting method that satisfies all of the…

A: Arrow's impossiblity theorem says that we cannot have a single voting method that satisfies all the…

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A: We first state the theorem (Theorem 10.6 in Apostols Analytic Number Theory) and then use the…

Q: Find the vertical and horizontal asymptotes. f(x) = -15 -10 -5 5. 10 -2 -4 -6p Step 1 -7x We are…

A: Solution

Q: Suppose r is a primitive root mod a prime p such that p = 3 mod 4. Prove ord,(-r) =

A: Given: p≡3mod 4 To find: ordpp-g=p-12

Q: Q3: Prove that, there is no simple group of order 200.

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Q: Prove that for all sets A and B, A – B = AN B

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Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: Problem 3 Let f(r) = x² + r. Use the limit definition of the derivative to compute f'(2). Find an…

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Q: 0, - 00<t<0 e at, 0<t<∞ Find the Fourier Transform of f(t)={ a is positive constant

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Qs: A. Define the symmetric group S3. Then find 1. Cent(S3) 2. All normal subgroups of S3 3. A3 4.…

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Q: 2. у"+2ху'+5у %3D0

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Q: prove by induction that fib(0) + fib(1) + ... + fib(n) = fib(n+2)-1

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Q: 4. Consider the following function: 2. -2 < x < -1 f(1) = {r, -1<r<1 1<r<2. 2-I, (i) Sketch the…

A: The graph of f is sketched as shown below.

Q: 1. Which of the following equations is the best/appropriate method to use in solving a system of…

A: We can use the Gauss-Jordan elimination method to solve a system with m equations and n unknowns.…

Q: 6.14 Table 6.1 (Weisberg 1985, Faithful Geyser in Yellows variables arex=duration c Can x be used to…

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Q: Consider sets A and B with |A| = 14 and |B| = 19. a. How many functions f : A → B are there? b. How…

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Q: Exercise 6.3.12. Suppose G is a group, a, b e G such that gcd(la\, [b|) = 1. Prove (a) n (b) = {e}.

A: Suppose (G,.) Is a group . Let , order of a and b is m and n respectively. Then am =e , bn =e .…

Q: A box contains balls: 3 red, 4 blue, and 5 yellow. A ball is hen randomly picked. What is the…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 4. Find the isolates singularities of the following functions, and determine whether they are…

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Q: (P → (Q → R)) ↔ ((P → Q) → R)

A: Given expression is (P → (Q → R)) ↔ ((P → Q) → R) We know that, a sentence is said to be a tautology…

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Q: Find the area of a surface given by Z=H+xyover a rectangular region defined by OSXSLand 0SXSW Momm m

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A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

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A: Given data field Fx,y=y-6x2,x+y2 around and across the triangle given by y=0, y=x and x=1.

Q: Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as…

A: Given :   D⊂ℝn2Let  A∈DThen  A = (a11 , a12 , ....... a1n , a21 , a22 , ....... , a2n , ...... an1 ,…

Q: cos t- sint i+ cos t- sint) sint+ cost) i+ cost- sint j, N = 1 j. and K= For the space curve below,…

A: To find- For the space curve below, T = cost - sint2i + sint + cost2j, N = -cost - sint2i + cost -…

Q: 2x 1+ 2e dx

A:

Q: 3. Determine a root of f (x) = -0.9x2 + 1.7x + 2.5 with an initial guess equal to 5. a. Use…

A: a)

Q: Solve for A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right…

A: We use properties of matrices.

Q: b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is…

A: (b) G is a group of order 2p.        Now, we know, order of any subgroup of a group must divide the…

Q: Suppose we have the following sets: J = N, K = {k E Z | 0 < 2k +1 < 20}, L = {0, 1, 2, 3, 4, 5, 6,…

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Q: Problem 1 Let Z denote the integers. Let S = {0 a,b e z} (a) Prove that S is a subring of M2 (Z) (b)…

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Q: Q14: Define subring. Is the set S = {(" is a subring of the ring M %3D of all 2 x 2 matrices?

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

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Q: Let a be an integer. ki k2 (a) Explain why if a? 1,.. ki ... pir, then k; is even for each prime p,…

A: The detailed solution using basic properties of divisibility is presented in the next step.

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Q: Q22 Find the Dual for the primal problem? P: Max yl + y2 Subject to: y1 + 2 y2 s 6 y1 - y2 s3 у1,…

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Q: If X is a finite dimension that an inner product o Yjk = (e, ex). Can we cho fashion? %3D

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Q: In the diagram, the cylinder and the hexagonal prism have the same height, h = 12 centimeters, and…

A: Solution :-

Q: Question 4 Suppose that for a certain product, the market price P = P(Q) can be written as a…

A: Given: P=500-QQ0=80 To find: a) P0 b) Strictly increasing Q0 c) dCSdQ0&gt;0

Q: Characterize the primes p mod 20 such ial

A: We have to characterize p mod 20 such that -5p=1.

Q: a) n(A) =    b) n(A∩B) =  c) n( B' ∩ C' ) =

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Q: Let X = {x E Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1 < 15}. Define a relation R from X to…

A: We have to find the elements of X and we have to define a relation R from X to Y.

Q: A point y in space either belongs to a given closed c ough y so that whole of the x lies in one open…

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