2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given e 2.7183, e 7.3891, e 12.1825) f(1.2). a and x 2.5 to approximate f (1.5) and (b) Use cubic Lagrange interpolation based on the nodes xo=0.5, x1 =1, x2 = 2 and x, = 2.5 to approximate f(1.5) and f(12)
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given...
Let f(x) = xlnx. Approximate f(2) by the Hermite interpolating polynomial using x0 = 1 and x1 = e and compare the error.(e ≈ 2.7...)
Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer
Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer
12 26 14 4. (15 marks) Let f(x)=/2x+1 . Use quadratic Lagrange interpolation based on the nodes x, 0, x-1 and x, 2 to approximate f(1.2)
12 26 14 4. (15 marks) Let f(x)=/2x+1 . Use quadratic Lagrange interpolation based on the nodes x, 0, x-1 and x, 2 to approximate f(1.2)
7.2 Let X have density f(x) = cx for 0 < x < 2 and f(x) = 0 for other values of x. a. What is c? b. What is F(x)? c. What are E[X] and Var[x]? 7.3 Let X have density f(x) = cx(1 - x) for 0 sxs 1 and f(x) = 0 for other values of x. a. What is c? b. What is F(x)? c. What are E[X] and Var[x]?
、
| | xo = 0 Xi = 2 x2 = 4 f(x) = 2 f(x1) = 6 f(x2) – 10 Consider the differential equation dy – Ax+ 4 where A is a constant. dx Let y = f(x) be the particular solution to the differential equation with the initial condition f(0) = 2. Euler's method, starting at x = 0) with a step size of 2, is used to approximate f(4). Steps from this approximation are shown in the...
5. Let f(x)- arctan(x) (a) (3 marks) Find the Taylor series about a 0 for f(x). Hint: - arctan(x) - dx You may assume that the Taylor series for f(x) converges to f (x) for values of x in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(x)? Show that the Taylor series converges at x-1. (c) (3 marks) Hence, write T as a series (d) (3 marks) Go to...
(a) Find the interpolating polynomials to the function f(x) = e-* sin(7x) at x = -1, 0, 1 and 2 using. (1) Lagrange's interpolation formula.
Let f(x) = e x − 3 define a real-valued function. Using an initial guess of w0 = 1, perform one iteration of Newton’s method to approximate the zero of f. Compute and simplify the error of your approximation.
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...