Show that the forward-difference approximation to d y / d x\fr... | Filo

Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h^2) to estimate the first derivative of the function examined in Prob. 4.4. Evaluate the derivative at x=2 using a step size of h=0.2 . 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. | Numerade

Find E(h), an upper bound for the error of the machine approximation of the two-point forward-difference formula for the first derivative. Follow the reasoning preceding (5.11). Find the h corresponding to the minimum of E(h). | Numerade