Solve the following problems according to the instructions

1. Using MATLAB determine the Taylor's Series of the following functions about a = 1 and containing five terms.(4 x 2.5 = 10 marks)
2. Sin (2x)
3. x⁵
4. e^2x
5. ln (x + 2)
6. Using Fixed-Point method for systems of equations, determine the roots of the equations

xy+ e^yx+ 5=14.39andx²y = 2

using five iterations. Compute also the approximate error for x and y values. Use MATLAB or EXCEL in your computations(10 marks)

1. Using high accuracy central difference equations, determine the derivative of the following function with ax=0.1. Determine also the percentage true error.

y = f(x) = e^2x+ x³

1. Using MATLAB, determine the integral of13(ex+x3) dx

Usex=0.5Use the Trapezoidal rule or Simpson rule

1. Solve the following ordinary differential equation using Euler's method. Use MATLAB/excel in your computations width ax=0.1. Find the value of y

when x = 0.5

dydx=x2/yinitial values: x = 1 ,y = 1