Show that the set of odd numbers is countable.

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

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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: 4. У(п) %3D [x1(п) * х2(п)] х1(п) %3D 26(п) + 56(n-2) х2(п) 3D 46(n-4)

A: Given y(n)=x1(n)*x2(n) Where x1(n)=2δ(n)+5δ(n-2)                (1) x2(n)=4δ(n-4)…

Q: Determine whether the improper integral converges or diverges. If converges, find the value. In x?dx

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Q: 6. Suppose an > 0, bn > 1 and lim an = 0, lim bn = 1. n-00 n-00 Define An = {x : an < x < bn}. %3D…

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Q: Factorise x6 + 1 as a product of three quadratic polynomials with real coefficients.

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Q: V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim…

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Q: t and W = Span -2 For what value of t is Let U = 1 3 the vector U orthogonal to W ?

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Q: Find volume of body bounded by z = x-y from below and z = x + y from Above inside y = x ,y 2.

A: Volume bounded by the region

Q: Exs Let PE-292]IR be function f(x)%={2 XEG -2 Showthat P3 R-integrable ornot?

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Q: [4 1 1 1] 4 1 1 You are given that the eigenvalues of A = 1 1 are 1 4 1 1 1 1 4 7,3, 3, 3, counting…

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Q: Let Y C R² be the set {(x, y)|0 < x < 1,0 < y < 1 and y E Q if x # 0} endowed with the dictionary…

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Q: Question 3 Let A be a 2 X 2 symmetric matrix satisfying A 9. and A 1 with the spectral decomposition…

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Q: Question 21 Let V = {(x, 4) x E R}. You are given that (V,O, O) is a vector space with (1, 4) Đ (72,…

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Q: +oo 22n (2x 1)". Vn2 +1 Consider the power series n=1 1. Use alternating series test to show that…

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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: 2. Use integration by parts to evaluate the following. (a) Sx tan-1 x dx

A: Given integral is ∫xtan-1 x dx

Q: 3- Vn -) Σ Vn3 n=1

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Q: You are given the data points (xi, Yi) for i = 1, 2, 3: (2,5), (1,9), (2,9). If y = a + Bx is the…

A: Given: A data points 2, 5, 1, 9 and (2, 9). To find: The equation y=α+βx by least square line that…

Q: [2 -2] 22 For A 1 0| and b -11 a least-squares solution of Ax = b 1 2 11 is â What is the…

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Q: ((x+1)ª-y² Consider the function g(x, y) = {(x+1)4+y²' -1, if (x, y) # (-1,0) if (x, y) = (-1,0)…

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Q: If AT = ul v. A and if the vectors U and V satisfy Au 5u and Av = 7v, then True False

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Q: B-8-8- 2 1 , U3 1 and W =Span{u1, U2, U3}. For 1 Let U1 U2 = 1 |2 -3 in W ? t what value of t is the…

A: Let us consider the vector space V  Spanning set of a vector space : A set of vectors that is used…

Q: Question 2 Find the inverse Laplace transform of H(s) =

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

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Q: What is the volume generated by revolving about the x axis the area bounded by the y = 2x +1, y = 0,…

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Q: 1. The velocity of a rocket is given by v(t)= 2000 ln 14x10 14x10 – 2100t -9.8t,0sts30 where v is…

A: Given vt=2000ln14×10414×104-2100t-9.8t , 0≤t≤30 and t=16, ∆t=2 and True value = 29.674

Q: If ffinite or in finite) Contable set, thers prave that At CS}=0

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Q: 3 Through polar coordinates, evaluate S S cos(x² + y²)ā dA, R where R is the region enclosed by…

A: The given question is related with evaluation of a double integral. We have to evaluate ∬R cosx2 +…

Q: A model created by an engineer is represented by the following multivariable functions x = t'u, w =…

A: As per Bartleby guidelines we're supported to answer only first three subparts. Kindly repost rest.

Q: 2. — 4х, + 2х, — — 6 4x1 2x2 Зх, — 5х, 1

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Q: Evaluate the Inverse Laplace Transform of the given functions. 1. F(s) s2+2s+1

A: Inverse Laplace transferom

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: [31 Consider the orthogonal basis B 10 of R. 51 Let v = -64 15 a If (v]B = |b what is the value of…

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Q: 1. x(n) = n(-1)²u(n)

A: Given clear step by step explanation

Q: Evaluate the Inverse Laplace Transform 1 F(S)=T51)(s+1)² (s-1) (s+1)²

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Q: Consider the following graph. 5- 4- Let u,(t) = u(t – 7) be the unit step function shifted 7 units…

A: Given: A graph To find: Express the function in the above graph in the form of y=f(t)uat+g(t)ubt.

Q: Г1 17 a Let A = 2 1 Find a QR-factorization of A. If R then the 1 3 value of a is the value of b is…

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Q: Consider the quadratic form f(x1, x2, x3) = x+ x+4.x+ 14x1x2. 1 is (i) The maximum value of f(x)…

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Q: Г2 0Т Г26 For A = |1 3 and b a least-squares solution of Ax = b is 1 51 . What is the least-squares…

A: A = 201331,  b = 2600,  x^ = 5-3 Least square error (e^) = ||b-Ax^||  Now, first find the value of…

Q: Consider the following graph. Let u-(t) = u(t – 7) be the unit step function shifted 7 units to the…

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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: Write TRUE if the statement is always correct and FALSE if otherwise. (a) If an >0 for all n E N,…

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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,…

A: The solution is given below. Hope this helps.

Q: Converges or Diverges?

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Q: x²y" + x(1+x)y' – (1 – 2.x)y = 0. II

A: Given differential equation is x2y''+x(1+x)y'-(1-2x)y=0           (1) By Frobenius method, let the…

Q: Let T : R² → R² be defined by 7(E)-E 2. X2 a If B = is a basis for R“ such that T'|B is a diagonal…

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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 8…

A: a) Set of integers between 1 and 50 that are divisible by 8 is: S=8,16,24,32,40,48

Q: Solve. S1 for 0 5 y" – 3y' + 2y y(0) = y' (0) = 0 The solution can be written as y(t) = f(t)u9(t) –…

A: The solution is given as

Q: Consider the function 3zy f(z, v) : (a) State the domain of f(z, v). (b) Find the limit 3ry lim (za)…

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