Functions : Convergence and Limits
Please see the attached file for the fully formatted problems. Let f be a real function defined by . 1) Evaluate f’(x), f’’(x), f(0). Show that f has exactly two roots and , with . Find an interval of two consecutive real numbers within which the roots must lie. From now on, let us denote and these two (closed) in ...continues
Questions on a Sequence of Polynomials. See attached file for full problem description.
I would like a short explanation of Gaussian Elimination with partial pivoting and Gauss-Seidel. Also, explain when each applies or when one is better than the other. Please include some examples.
Relation S is defined as followed: xSy iff y-x is an integer (x,y € R) where R=all real numbers a) prove that S is an equivalence relation on R b) Which real numbers belong to [-17]?
Please see attachment. C(A) stands for C'infinite'(A).
Eigenvector Estimation : Inverse Power Method
Please see the attached file for the fully formatted problems. Use the inverse power method to estimate the eigenvector corresponding to the eigenvalue with smallest absolute value for the matrix -1 -2 -1 A= -2 -4 -3 2 2 1 where X0= [1,1,-1]. In finding A-1 use exact arithmetic with fractions. ln applyi ...continues
Using Matlab to solve non-linear equations
Hi, I need help in using Matlab to build an m file for solving non-linear equations using the Newton-Raphson method (or another recommended method.) I need a clear explanation of the process of creating an m file, and also using it to find the roots of the following two equations as examples: 1) f(x) = exp(-x) - sin( ...continues
Solve the equation tanh(1/x) / (1/x) = 0.95 Using the graphical, Bisection, Newton-Raphson, Regula Falsi or Muller methods. Solve the equation 1+1/[cos(x)*cosh(x)] - ax*[tan(x)-tanh(x)] Using Mueller's method
please see attached pdf.
Chebyshev ploynomial of degree 4 interpolation
Calculate the five Chebyshev nodes in the interval [-1,1] which are used when interpolating with a degree four polynomial. Evaluate the function f(x)=2arcsin(x) at each of these points. Construct the degree four Chebyshev polynomial. Evaluate the resulting polynomial at x=0.8 and compare with the actual value of the function.
