Using Backward divided difference with a step size of 0.01, the second derivative of f(x)= 5e2.3x at x=1.25 (Use four digit rounding) is
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Using Backward divided difference with a step size of 0.01, the second derivative of f(x)= 5e2.3x...
Numeric Analysis
1) Letf(x)=- 2x x2-4 a. Approxi the first derivative using central difference and the second derivative mate at x= 1.25 using and h=0.25. (Use 4 decimal digits using backward difference rounding). Approximate f f(x)dx using trapezoidal rule with h-0.5 (Use four decimal digits rounding) c. Approximate S fCx)dxusing 1/3 Simpson's rule with h-0.25 (Use four decimal digits rounding)
Chapter 2.02: Problem #3 Using forward divided difference scheme, find the first derivative of the function f(x) - sin(2x) at - x/3 correct within 3 significant digits. Start with a step size of h 0.01 and keep halving it till you find the answer. ее NOTE #1: The above mentioned problems are taken from the book: Numerical Methods with Applications, 2nd edition, by: A. Kaw& E. E. Kalu
Estimate the second derivative of the following function using stencils for the FORWARD and CENTRAL derivatives for an order of accuracy of O(h2) for each. Use a step size of h -1. fo)x-2x2 +6 Second derivative, Forward Difference Approximation, o(h2)- Second derivative, Central Difference Approximation, O(h2) Which of the two methods is closer to the true value? (Forward/Central 12.5 points Differential Equation Estimate the second derivative of the following function using stencils for the FORWARD an derivatives for an order...
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the first derivative of the following function:f(x)=25x³-6x²+7x-88Evaluate the derivative at x=2 using a step size of h=0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
Suppose we needed to calculate the second derivative of f(x) = log(x) at x=4. Use a forward difference scheme to find an Oſh) approximation with a step size Ax=0.21. The log used in this problem is natural log (base e). Input your answer to four decimal places.
Compute the backward and center difference approximations for the 1st derivative of y = log x evaluated @ x=20 and h=2. Using the second order error O(h2) formula.
5. Create a MATLAB script to find the first and second derivative of given function using Forward, Backward, central and Taylor numerical schemes. Test your code using the following functions: f(x)-xe*+3x2 +2x -1 and find f (3) and f' (3) for with h 0.1, 0.01 and 0.001 b. Approximate y'(1) and y"(1) using the following table f(x) 0.992 0.8 0.9 0.999 1.0 1.001 1.008 Input: (copy and paste the MATLAB or Scilab script in the following box)
5. Create a...
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error) of the numerical approximation of the derivative in each case.
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error)...
Use the truncated Taylor series of fourth order and show that the fourth order backward finite difference formula is fa)(x)- 4f(x - Ax) + 6f (x - 2Ax)- 4f(x - 3Ax)+ f(x - 4ax) (Ax) Next, use this formula to find f(4(2.165) in six decimal places if step size Ax and f(x) cos-1(0.1x + 0.42). 0.01
Use the truncated Taylor series of fourth order and show that the fourth order backward finite difference formula is fa)(x)- 4f(x - Ax) +...
please show the matlab coding
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.