Q2) Q3) a) Find the root of the equation xlogx=1 which lies in between 2&3 correct to 3 d.p using Regular false method. b) Compute the integral 1=√(x²+3)dxusing Simpson's 3/8 rule for n=3 c) Using Taylor series obtain the power solution of the initial value problem y¹ = x²-y²,y(0)=1 the powers of x a) Find the root of the equation f(x) = x²-3x²+2 in the vicinity of x=0. Using Newton Raphson method correct to 4 d.p b) Given the equation = x² - 3x + 1 with y(1)=2 dx Estimate y(2) by Euler's method using i) h=0.5 CAT 2: ii) h=0.25 -5 dx So a) Find an approximate value of loge by calculating √ 4x4 by Simpson rule of integration use n=10 b) Solve the given initial value problem using modified using modified Euler method for value of y at the given point x with given h. y¹ = 1+ (x + y) at the point x=0.2 h=0.1

Q: Q1) Solve the following equations by the power-series method: A) xy - (x+ 2)y' +2y = 0

A: As per the guidelines I am supposed to do only one question. kindly repost the other question…

Q: b)If (x) = f(x+2n), find the Fourier series expansion of (0, -n SxS0 x, 0 SxSn f(x) = %3D

A:

Q: Q1) Solve the following equations by the power-series method: A) xy – (x + 2)y' + 2y = 0

A: Solution for part A: Given differential equation is xy''-(x+2)y'+2y=0           (1) let the solution…

Q: Expand, f(x) = -1 f(x) = Sinx f(x) = +1 (MXN) (n≤x≤-1/2) (-≤x≤) in a complex Fouriér Series if the…

A: As per the question we are given a piece-wise defined function f(x) with period of 2π and we have…

Q: If dy/dx=2xy - 8x passes through (1) A) Find f(1.2) with two equal steps by euler's method.

A:

Q: 2--solve the Fourier series for the function f(x) = 3- x ,and -n < x < T. A:f (s) =+E-1 4(-1)"Tsin…

A: Concept:

Q: Solve xy" +(1- 2x)y` +(x-1)y =0 using power series method

A: Given that xy''+(1-2x)y'+(x-1)y=0 Take y=a0+a1x+a2x2+a3x3+a4x4+a5x5+...... Take the derivative,…

Q: 4. Find the first three nonzero terms of the Taylor series of the function f (x) = sin x in the…

A:

Q: Solve for the value of f(x) = e³x² Using 12 term Taylor series if x = 0.056

A:

Q: Q4. Find the Fourier series for f(x)= A – x _in the interval (0, 27). Deduce that 111

A: Let fx=π-x To find the Fourier series for fx in the interval 0,2π and further deduce…

Q: Find the solution to the ODE using power series solutions   (x-1)y''+3y=0

A:

Q: Given the triangle above, find the following: Round all answers to 3 decimal places as needed. B…

A:

Q: Find the taylor series for f(x) = -4ex about x=5

A: The Taylor series of a function f(x) is given by  f(x)=∑n=0∞fn(a)n!(x-a)n Here, the given function…

Q: Calculate the Taylor polynomials T2 and T3 centered at x = a for the function f(x) = In(x + 1), a =…

A: Given function is  fx=lnx+1. To calculate Taylor polynomials T2 and T3 centered at x=a, we write…

Q: 6. Given F(x, y, z) = (8x° +z²,-3z, 2xz – 3y), a) Determine whether or notF is a conservative vector…

A:

Q: Pls solve this question correctly instantly in 5 min i will give

A:

Q: Date.... x x) pO od { (x) = x 37

A:

Q: numerically greatest

A:

Q: FIND THE SOLUTION OF THE EQUATION USING THE FROBNIUS SERIES 2) 2xy" + (x+ 1)y' +3y 0

A: According to guidelines we expert can solve only one question at a time, please repost other…

Q: 8) a) Find the first few coefficients for the Fourier series for, F(x) = X on b) Comment on the…

A: Given: The given function is Fx=x on the interval -π,π. Formula to be used: The formula to calculate…

Q: Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on…

A: (a) Given that F(t)=2tF(−t)=−2t=−F(t)Therefore F(t) is an odd function.F(t) extends to [−π,π] so the…

Q: x' + 2e* – In xr- 3 = 0

A:

Q: 1. A power series is a series of the form and cn's are where x is a 2. The power series can be…

A:

Q: 2. Use bisection method up to seven iterations x-2x³-4x²+4x+4=0 on the interval [-2, -1]. to find…

A:

Q: etermine the coefficients of the x3 term of the Taylor series about the point 0 of the function f(x)…

A:

Q: 3. Calculate the Fourier series up to and including the third harmonic in'terms of the secondary…

A: Given: To calculate the Fourier series up to and including the third harmonic in terms of secondary…

Q: 5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0…

A:

Q: Part A) Use the Taylor series expansion of sin x to write sin(√(t)) = t^(1/2) - (t^3/2)/3! +…

A: We see the Taylor series expansion of sin x to write sin(√(t)) = t^(1/2) - (t^3/2)/3! + (t^5/2)/5! -…

Q: FIND THE SOLUTION OF THE EQUATION USING THE FROBNIUS SERIES 1) ry" + 4xy' +2y 0 2) 2xy" + (x + 1)y'…

A:

Q: expand the function f(x) = sin(x) / (coshx +2) in a taylor series around the origin going up to x^3.…

A: Taylor series of function f(x) around x=a is defined as:

Q: Q2: Based on series solution of Legendre Equation (1-x)y"- 2xy'+ ((l+1)y=0 Find Legendre Polynomial…

A: We solve this using power series of differential equation

Q: What is the 7th term in the Taylor series for f(x) = 5e5* taken about x 7th term = 7-6-5-4-3-2-1-36…

A: