Q1: Find the Fourier series of the following functions form>t> 0 ₁. ƒ (0) = { ²/₁2 1 for 2n>t>n 2t 2. f (t) = { 0 3. f(t) = { - 1} for 1>t>0 for 2 > t > 1 for-1

Q: If y₁ and y2 are linearly independent solutions of t2y" + 4y + (5 + t)y = 0 and if W(y₁, y2)(1) = 5,…

A:

Q: Let G and H be groups and let :G →H be a homomorphism. a) Prove that (G), the image of p, is a…

A:

Q: dP/dt + 2tP = P + 6t - 6 a) Find the general solution of the given differential equation. b) Give…

A: Given data: dP/dt +2tP =P+6t-6 To find: (a)General solution of differential equation (b) Large…

Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

A:

Q: Determine the intervals in which solutions are sure to exist. t(t − 2)y(4) + e¹y" + 6t²y = 0 Enter…

A: As per the question we are given a forth order linear differential equation as : t(t-2)y(4) + ety''…

Q: Determine h if V = 1.1535 m³ and r= 1m using Fixed point iteration on the given convergent equation.…

A: Given function is h=h3+3Vπ3r We have V=1.1535 m3, r=1 m. So we have h=h3+1.1023 For more convenient…

Q: siven that 2₁ ³ / ( : ) · (61) and 24 (1) is a subspace of IR ³ Find a basis for 2, 12₂ and Find dim…

A:

Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

A:

Q: The eigenvalues of the matrix are: -1, 1, 2 0, 1, 2 3, 0, 0 1, 1, 1 1 1 1 1 1 1 1 1 1

A:

Q: 4. 1 3 2 3 1 6 5 4 5 9785 Given the matrix A2 (a) Find a basis each for N(A) and C(A). What is the…

A: For the detailed solution of the problem follow the next steps.

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Sol:- y''' +y' =tantThe general solution to anxyn+...+a1xy'+a0xy=gx can be written asy=yc+ypyc is…

Q: Given the following recurrence relation, determine the first two terms of each of the two linearly…

A: Given is a recurrence relation as c2=-4c0     and     ck+2=2 ck k-4k+1 k+2 for k=1, 2, 3, ...   To…

Q: Let A = {0, 1, {0, 1}}, and let B = {0, {o, {0}}}. Then the cardinality of P(A x B) is A. 128 B. 64…

A: Correct answer is 64. Explanation is as follows

Q: Five stacks of cubes are given below. umbers of cubes in the stacks are 4, 2, 6, 10-nd 8 (a) Move…

A:

Q: a) The equation that gives the temperature in (K) for a particular hot body is given by : T3-0.16572…

A:

Q: ts Integrate using an appropriate method. State whether this integral is convergent or divergent.…

A: Sol:- ∫-121x3dx If exist b, a<b<c, fb=undefined, ∫ac fxdx=∫ab fxdx+∫bc…

Q: Calculate the present value PV of an investment that will be worth $1,000 at the stated interest…

A:

Q: Let G be a graph with 20 vertices and 46 edges. Suppose the degree of each vertex in G is either 4…

A: We use Handshaking Lemma.

Q: Consider the matrix A = 5 1 0 5 1 0 l-1 1 6 a) Diagonalize the matrix in the form A = SAS-¹, with S…

A: Solution a) Given matrix is A=510510-116 Let the eigenvalue be λ, then…

Q: Consider the following initial value problem: x" - 5x²14x = sin(8t), x(0) = 2, x' (0) = -1. Using X…

A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

Q: Use the division algorithm to find q (x) and r(x) such that a(x) = q (x) b(x) +r (x) with degr(x)…

A: Here the solution for q(x) and r(x) in Z7[x] are  q(x)=5x2+2x+1r(x)=6

Q: y" - 10y' +9y = 5t, y(0) = -1 y' (0) = 2

A:

Q: 20 An excavator shown in Figure Q1 (b) was in an equilibrium position. Assume support/connection at…

A:

Q: Suppose that China's population policy is modified so that every family could have children until…

A:

Q: B/ Given a polynomial function with following data points: Find x f(x) 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6…

A:

Q: {Q.B} 5 e change of coordinates matrix from the standard basis E of R² to the basisi B Given the…

A:

Q: 1. 1 3 2 3 1 6 5 4 5 39785 Given the matrix A= 2 (a) Find a basis each for N(A) and C(A). What is…

A:

Q: 1. How many elements are there in Z 2. List all elements in Zis 3. Answer either'true' or "false"…

A:

Q: Use an appropriate test to determine whether the series converges. Σ k=4 3 1 -6k+24

A: Given series is ∑k=4∞1k3 - 6k + 24

Q: Find the solution of the initial-value problem y" - 3y" + 4y - 12y = sec 2t, y(0) = 2, y'(0) A…

A: Given y'''-3y''+4y'-12y=sec2t, y02, y'0=-12,y''0=232

Q: Define the mapping 7: R²→R by π((x,y))=x. (Note that R is a group under addition with identity 0).…

A: Here we use the definitions of group homomorphism and the kernel of it . Which are given in solution…

Q: Solve the the following recurrence relation using an appropriate method Un = 3Un-1 + 4Un-2 with Ug =…

A:

Q: 6. For the function, f(y) - b+y³¹ y² b+y³¹ (a) Find a power series representation for f(y) = b>0.…

A:

Q: 2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dr. Define the func- tions fi(x) = 1,…

A:

Q: (b) If you walk northwest, will you start to ascend or descend? O ascend O descend At what rate?…

A:

Q: x 0.1 0.2 0.3 0.4 0.5 0.6 f(x) 0.62049 0.28398 0.00661 0.24842 0.32513 0.45789 Compute…

A: Given the data: x 0.1 0.2 0.3 0.4 0.5 0.6 f(x) 0.62049 0.28398 0.00661 0.24842 0.32513…

Q: d²y d 0dw 0 m (m) stanierarbadoid-mon Transform the equation by the substitution x= 1 and show that…

A:

Q: 7. 1 -4 Let A -2 3 4 -8 2 (a) Show that A is diagonalizable and find a nonsingular P such that P-¹AP…

A: Q-7 (a) The characteristic equation is |A-λI|=0, which implies 1-λ-4-2-23-λ24-8-5-λ=0By solving…

Q: Use the Limit Comparison Test to determine the convergence or divergence of the given series. a b iM…

A:

Q: Show X n² n² +1 is a Cauchy sequence using the definition.

A: We have to check weather the given sequence is cauchy sequence or not.

Q: 2. Equip C[0, 1] with the inner product (f 1g) = f(x) g(1) dr. Define the func tions fi(1) = 1,…

A:

Q: Could you please solve d) too

A: given matrix  A=510510-116 find the transpose AT=55-1111006 (d) determine if the matrix A+AT is…

Q: I cant understand this please post and write it on a paper

A:

Q: Q1 Test the convergence of the series Σ=o(−1)n+1 (n!)² (2n)!

A: Given series is convergent. Explanation is as follows

Q: Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For…

A:

Q: The relation R₁ = {(a, b) = N²: alb} symmetric. O True False

A:

Q: Times Absent Final Mark 77

A: From the given data we have to find the equation of the best fit line, correlation coefficient,…

Q: Find a general solution to the given differential equation. 24y" - 13y' - 2y = 0 What is the…

A:

Q: there was a flood. The total cost to replace her damaged belongings was $1,760.00. What percent…

A: Given insurance policy is $19.00 per month for 15 months Damage cost is $1760.00. We have to find…

Q: Solve the differential equation by variation of parameters. 1 y" y² + 3y + 2y = 2 + ex

A: