.s) Prove that k = n kn (a) fel(k-n)wot dt = ST = to +00 (b) If x(t) = Σake/kwot and T = 2π ; then an = x(t)e-t Wo

Q: Suppose that U₁,...,Uk are subspaces of V. Prove that V = U₁ ☺ · · · ÐUk if and only if the…

A: Please find the attached solution

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e¯², y =…

A:

Q: 4. Prove that in any party (with at least two people), there are always two people in the party with…

A: Consider a party with n people Each person is ether friend or not friend of the other n-1 people in…

Q: Let G be a bipartite graph of order p. Then i(G) ≤ 2.

A: please find the attached image

Q: 8. Find the Eigen values, corresponding Eigen vectors, and Eigen spaces of the following matrix A =…

A:

Q: Assume that a sequence of integrable functions (fn)n converges pointwise to an integrable function…

A: Please find the attached answer

Q: (a) 64x 56 (mod 52) (b) 14x = 35 (mod 56)

A:

Q: Let V be a a) Show that im(S+T) is a subspace of im(S) + im(T). b) Show that rank(S+T) ≤ rank(S) +…

A: It is given that,  V be a finite dimensional vector space and  S, T ∈ LV. We have to show the…

Q: 2. 4y+12y+10y=16x-50 cos 2.x

A: Solution to the differential equation using short cut formula method.

Q: Consider the sequence (an) given by the recurrence an+1 = 2an-n for all n € N, with the initial…

A: We will find the pattern of a1,a2,.....,a6, the we can predict the general formula.

Q: 5. (a) How far must a zonal ring of air initially at rest with respect to the earth's surface at 60⁰…

A:

Q: f(r,0) = e-to Find the regions where f is the analytic function Consider the function

A: Given that     f(r,θ) = e-iθr Since  fr,θ = ur,θ + i vr,θ  and  e-iθ = cos(θ) - i sin(θ)…

Q: Use Weiestrass's definition of limit to show that lim (7x - 3)= 32. x-5

A:

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: der the initial-value problem dy dz = 1+2x-3 find the approximation of y(2) with the step size h =…

A: Here, in the question, it is given the initial value problem as: dydx= 1+2x-y, y(0) =1 We have to…

Q: Let A, B E Rnxn and let R[x] be the set of all polynomials in variable x with coefficients in R.…

A:

Q: How many integers in between 1 and 3000, inclusive are divisible by either 5 or 7?

A: Let A and B are two sets such that then number of elements in A and B are obtained as…

Q: Determine if the following sequence converges. If it does, find its limit. 8 √2n! \ (2n)! (n=1 2.…

A: (1) Let, the given sequence is {un}, where un = 2n n!2n!

Q: Assume that a sequence (fn)n of integrable functions converges strongly to an integrable limit f.…

A:

Q: Find the family of graphs G of order p such that y(G) = p.

A: Please find the attached solution

Q: Question # 1: A function is given by f(x) = 6e-3. Now Answer the following: 1. Calculate f'(x) at x…

A:

Q: f G is a group and H is a subgroup of ind how that H is a normal subgroup of G.

A:

Q: A matrix A= -12 20 -3 -4 -8 4 400 4 0 40-4 0 01 1 - 11 Find a basis for Nul A: - 8 -1 -5 -1 3…

A:

Q: prove that the sum of four consecutive integers is even.

A:

Q: Find the Laplace transform of the periodic function f(t) whose graph is given below. --1 1.0 -1 1,0…

A:

Q: 4. A tank contains 80 gal of pure water. Brine solution with 2 lb/gal of salt enters at 2 gal/min,…

A:

Q: ydx - xdy + 3x²y²e*' dx = 0

A:

Q: t²y' + 2ty - y³ = 0

A:

Q: 1 dx 2 21+2*2 ху

A:

Q: = (4) Let ER and fn = XAn, where An j+2k = n. Compute fe fn in terms of k and show that (a) the…

A: Pleas find the attached answer

Q: O Solve the following initial value problem: dx dt dy dt = = 2x + 5y 2x - y x(0) = 1, y(0) = 6

A:

Q: Delaney is about to take a final exam that consists of 20 questions. To motivate her to study, her…

A:

Q: Line L, is parallel to vector a = -31 +23+4k and passes through a point A(7, 6, 2) and line L₂ is…

A:

Q: For Newton's Method, y = x^d. How d will influence the convergence of Newton's method?

A:

Q: f G is a finite group and Z is its centre, then class equation of G is expressi o(G) o(G) = o(Z) + E…

A:

Q: Solve the followig non linear gebraic equation to fined one non Zevo root. P(x) = Sin [√ Secx + x…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: Question 2 Rewrite the product using product notation. (34) (45) (7.8) (10:11)... (4950) 51-52 Hint:…

A:

Q: a. What is the trapezoid approximation with n subintervals? T(4)= (Round to six decimal places as…

A: Let the given integral  I=∫1e6xdx   Take y=fx =…

Q: 3. Let R-Z18. Determine the units and zero divisors of R giving the explicit unit or zero divisor…

A: We know that  no of units in ring Zn = phi(n), and  no of zero divisor of Zn = n - phi(n) -1

Q: D(G) If G is a finite group, than o(G) = Σ- o(N(a)) where this sum is taken over one element of each…

A:

Q: 2. If A is a 3 x 3 matrix, prove that the determinant of A is equal to the determinant of AT.

A:

Q: c. 6-3

A:

Q: (b) Let G=(Z8, +) and f: GG be defined by f(x) = 2x and show that f is a homomorphism that is…

A:

Q: -Solve the above linear system, by using the Gauss-Jordan reduction after you substitute k value…

A: We will apply elementary row operations on augmented matrices.

Q: Let a) Use the fact that the Find the domain and range of b) show that tp (x) = 6² is decreasing…

A:

Q: Question 1 differential equation Consider the following 1 dy x² dx 2 + · y = x3 x5e-3x y-4

A:

Q: Part a) Rewrite by peeling off the first term and the last two terms. n+1 k (k+1)! Part b) Rewrite…

A: Given that, ∑k=1n+1k(k+1)!   Consider the first term and last two terms in expansion as follows:…

Q: u, respectively, and x, y and z are unit vectors along the bis

A:

Q: f(x, y) = x²-y. Sketch 4 level curves of f(x, y).

A: As per our company policy, we are supposed to answer only the first question for you. Kindly repost…

Q: In the figure above, if - what is the value of r? r=

A: