Sin(x) in( at x -0.5 using Richardson's Q5: Evaluate numerically the derivative of f(x)-x extrapo...
Write a C program that numerically calculates the second derivative of the function f(t) = sin(H) + 0.3A where the input&ranges [0:0.1:5). Find the second derivative at each point not including the first and last points. Also calculate the analytical solution at each point. Print to the screen the numerical and analytical results for comparison
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
. Use Richardson's extrapolation method to compute the derivative of fx)- e' sinx) at x - I with initial Δx = 0.1. You should carry out the extrapolation steps until the computation for Ax-0.025 completes, and clearly indicate the desired answer. You should show all computation steps. Only providing an answer and/or using a wrong method receives zero point.
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate af/az. Э//ду, and Эг f/0гду) at x = y = 1 numerically using 2nd-order central difference formula with a grid spacing h -0.1. Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework...
2. Given f(x)=e*: (a) Find f'(x) using the definition of derivative, f'(x)= lim{{(x+h)-f(x)), by making h smaller and smaller. Round answer to two decimal places. (b) Evaluate f (1). (c) Carefully, graph f(x)=e-*, -15x52 using points every 0.5 units. (d) Find the equation of the tangent line at x = 1. Attach the graph of this line to the graph in (c).
python the polynomial equation is Ax^3+Bx^2+Cx+D b) Evaluating a polynomial derivative numerically For a function f(x), the derivative of the function at a value x can be found by evaluating f(x+2)-(*) and finding the limit as a gets closer and closer to 0. Using the same polynomial as the user entered in part (a), and for the same value of x as entered in part (a), compute the limit numerically. That is, start with an estimate by evaluating** 72 using...
Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at x = 1.5 using x = 0.1
Evaluate the derivative of the following function. f(w) = sin [cos - (7w)] f'(w)=
To Be Done Only in MatLab Please use the format provided: The derivative can be computed numerically using the definition of the differentiation. with a small For example, derivative of f(x) = x, for () 1 with h = 0.01 is given by x x= 0:0.01 :1; Note that, diff(x), for a vector X, is [X(2)-X(1) X(3-X(2) Xn)-Xn1) So diff gives you one fewer points 2 for-2 IS 2 with h-0.01 . Then plot f(x) and g(x)-rx) Use the above...
3) Use L'Hopital's Rule to evaluate and check your answers numerically: - sin x (a) lim x+0+ х 1 (b) lim X-70