(a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

Q: 4. Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for…

A: To find- Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial…

Q: 1. a) Find the Riemann sum of f (x) = x² – 3x + 2 over [2, 4] for the partition given by 2 = xo <x1…

A: We know that Riemann sum of a function f(x) using right endpoints over the interval [a, b] is…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: The approximate Riemann sum of f(x) = x³ - 9x on [0, 8] using n rectangles with right endpoints x;…

A: We have to find the value of f(8i/n)

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: Prove that the effective factor is a Hermitian factor in a specif and x-i

A: Momentum operator is defined as an Hermitian generation of translations, then it is hermitian by…

Q: 4. Use the error formula to find a bound for the error at a = 0.31 in approximating a sin(2x-5+1 on…

A:

Q: 4. Let z = -4 + 3i and zw = -7– 2i. By showing clear steps, find w in the form of a+bi.

A:

Q: ¤1 + ag – r3 = 0, -2r1 – 12 + 5r3 = 0, -#1 + 4.x3 = 0 find the Rank(A), where 1 1. -1 A = -2 -1 -1…

A:

Q: Use De Moivre's Theorem to find the fourth root of Z = 8i(3 + v2).

A:

Q: Determine the minimal polynomial for cos(π/3) + i sin(π/3) over Q.

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: 6. Find the Maclaurin seriés for f(r) = (1-x)-2. %3D

A:

Q: 61. Prove Theorem 4.13(c): For any real numbers a and b, Si x² dx = (b³ – a³). Use the proof of…

A: To prove : for any real numbers a and b,∫abx2dx=13(b3-a3). Solution: We know, ∫xndx=xn+1n+1+C…

Q: Applying the Cauchy's Residue Theorem, evaluate de (5 – 3 sin 0)²

A:

Q: 2. Find the Maclaurin polynomials of order n=0,1,2 for f(x) = cos(x).

A: Consider the formula for Maclaurin series: Calculate the derivatives to find the terms in the…

Q: Part (b) 5e Evaluate -dz by residue theorem, where C is the contour |z| = 2 6z4 +30z3

A:

Q: 2. Find the rank-1 approximation of A and its approximation error with respect to the spectral norm…

A: Given: Calculate A's rank-1 approximation and its approximation error in terms of the spectral norm.…

Q: Determine the third and fourth Taylor polynomials of cos xat x = π.

A: Determine the third and fourth Taylor polynomials of cos xat x = π. Given, f(x) = cos x at x = π.…

Q: -3 Compute the coefficient Fourier an of the f(x) = { -1<x<0 0<x<1

A: Apply the concept of even - odd function and very easily guess the solution.

Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: 1 Expand in ascending powers of x, up to and including the term in x', simplifying the V(1 –2x)…

A: To solve the following problem

Q: 1. Determine the discrete least squares trigonometric polynomial S2 (x) on the interval [-T, 7] for…

A:

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: 1. Write the finite difference approximation of u – uxx = 0 in the explicit method used to solve…

A: The complete solutions are hoben below.

Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: Find Fourier expansion for the function f(x)= x-x², -1<x<1.

A: We are asked to find the Fourier series expansion for the following function: fx=x-x2,…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: 1. Find a formula for A" using the diagonalization process (A" = PD' p'). Show all the work.

A: We need to diagonalize the matrix.

Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

A:

Q: 7. (a) Find all the values of z such that e = 1+ i.

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have given  y'=2x-3y+1   ,y(1)=6 we know that Euler's formula…

Q: z with respect to z at the point 4.

A:

Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

A:

Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: We have to use the Euler method

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: Jse Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: Given: dydx=2x-3y+1, y(1)=6 f(x,y)=2x-3y+1, x0=1, y0=6, h=0.1…

Q: Suppose &lt;let A= 1 and you know all the cofactors in C. How can you find A?

A: Given: Determinant of a matrix A  =  1 and all the co factors are known.   To find: The matrix A.

Q: Verify that the functions f1(x) = 1, f2(x) = sin x, and f3(x) = cos x are orthogonal in [−π, π], and…

A:

Q: here the spacing is suc

A:

Q: The characteristic of Z5[x]/ is

A: Introduction: Suppose, Rx be a ring of polynomials and Px be any polynomial. If there exists an…

Q: At z = 1, find the residue of 1/ [z(z-1)]

A:

Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

Q: a) Show that u(x,y) = x3 – 3xy2 + 3x2 – 3y2 is harmonic and find its harmonic conjugate

A:

Q: Let A={(-1)" Find sup A and inf A. Provide some explanations how you got their values or why they…

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.