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Q: Evaluate the Inverse Laplace Transform S-1 F(s)= (s1)(s?1)

A: The solution is given as

Q: Question 32 f 3 4 - Let S = 1 3 -7 1 8 -17 Which of the following statements describes the set S?…

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Q: Question 13 Let T : R? → R*be defined by 1. 8 T X2] x2] .2 If B = is a basis for R´such that T B is…

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Q: Given the following sets: U=(set of real numbers) %3D A = (x| x is a positive real number) %3D B =…

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Q: = the power series ) 22n (2.x – 1)". Vn? +1 ermine the radius and interval of convergen ce of the…

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Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to…

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Q: +00 (5 – 4(ln n)³)" Σ (V3 . In n)3n n=2

A: Given series is ∑n=2+∞(5-4(ln n)3)n33·ln n3n

Q: Question 31 2 1 1 U2 = 1 and W =Span{u1; U2, U3}. For 1 Let Uj = Uz = 1 1. 6. in W ? what value oft…

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Q: Show that the set of odd numbers is countable.

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Q: (-1)" Given: sin x x2n+1 for x E R 2 (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

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Q: Suppose that A is a 14 X 9 matrix that has 6 pivot columns. Then: (1) dim(ColA) is (ii) dim(ColA)+…

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Q: Let (V, (, )) be an inner product space and let f, g be vectors in V. if || f|| = 4, ||| 5 and || f…

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Q: 1. Let C be the curve with parametric equations V2 - t? 3/2 8 1 Y = t + 3 where t e [0,+). V2 8 (a)…

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Q: Suppose that x is an eigenvector of a matrix A with corresponding eigenvalue 6. Then x is an…

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Q: QI) Evaluate the integral f dy dx using polar coordinate

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Q: 1 List the elements of each of the (a) The set of integers between 1 and 50 that are divisible by e…

A: We have to right the givens sets into roaster from of set notation.

Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) : = 7 and |w| = 5,…

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Q: 1 3 01 a Let A = 1 5. If 6 is in NulA, -1 4 -7 [2 | then the value of a is and the value of b is

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Q: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 0,

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Q: [8 1 3 7] 0. 5 k 4 Let A . If the dimension of the eigenspace corresponding 0. 0 8 5 0 3 0. to…

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Q: (4-x)". /n 00 n+5 9n : 7" n=1

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Q: Let n = pq be the product of two odd primes. Recall that there are no primitive roots modulo n. Show…

A: We use the idea that if primitive root exists then x^2 = 1 mod (m) has only 2 solutions. The…

Q: 2 0 01 Let A = |0 1 4 0 4 1 Which of the fallowing statements is TRUE about the quadratic form f (x)…

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Q: Let H = Span{1 +x²,1+x,1+x + a²,1+2x – 2x²}.What is dim H?

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Q: to evaluate the function using reversed order of integrati 1 eее-x dx dy 1 Jin y

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Q: Solve for the laplace transform  x(t) = 3(t-5)5

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Q: Evaluate the Inverse Laplace Transform F(s)= s+ 3s + 2

A: Problem is solved using concept of inverse laplase.

Q: (a) If an 2 0 for all n E N, then an does not converge conditionally. n=1 (b) If the power series >…

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Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) = = 7 and w= 5, then…

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Q: Question 5 Suppose that A is a 16 x 14 matrix that has 6 pivot columns. Then: (i) dim (ColA) is (ii)…

A: Given that A is a matrix of dimension 16×14 that has 6 pivot columns. Then  (i) dim(ColA)=number of…

Q: Question 18 Let B = {1+x, 1 – x2, x + 2x} and p(a) = 7+ 10x + 11a?. You are given that B is a basis…

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Q: Question 29 Let (V, (,)) be an inner product space and let f, g be vectors in V. If ||F|| 4. ||g|| =…

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Q: Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) =…

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Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions f(x, y) =…

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Q: Which of the following vectors are not linearly independent? Non of these

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Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin -0) +1 in…

A: 4. To Find: The Plane area inside the polar function r = 2 and outside the polar function…

Q: 3. 2х, — х, = 2 х, — Зх, + х; 3 — 2 -x, + x2 - 3xz - 6 %3D

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Q: Evaluate cxy)dA av)d4 over the region R bounded by y = 2r, y=x+1 and x = 3. (3, 6) 5.5+ y-2x 4.5+…

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Q: In(n)

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Q: Question 4 2 1 1 1 Let V1 = V2 = 3 V3 = 1 V4 = 1 4 8 For what value of t is the set V1, V2, V3, V4}…

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Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

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Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

A: We have to explain the given statement.

Q: +o0 Consider the power series 22n (2x- 1)". Vn2 +1 n=1 3. Determine the radius and interval of…

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Q: Question 18 Let B = {1+x, 1 – x2, x + 2x} and p(a) = 7+ 10x + 11a?. You are given that B is a basis…

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Q: [1] Construct a 2 × 2 symmetric matrix A such that A 3 and -2] -2 8 a11 012 If A = a21 then the…

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Q: H.W: Evaluate the follou

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: [2 1 1 V2 = 3 1 V4 1 Let Vj = , V3 1 4 1 2 8 For what value of t is the set {v1, V2, V3, V4} NOT a…

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Q: Evaluate: f (3x2 - 20x)² dx

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Q: Given do = and di = Then de and d, are G- conjugate if Gis %3D Non of these O D [4 21 l2 8l O A B.

A: We want to find the matrix for which the given vectors are G-conjugate