Hi there looking for help to understand these questions and explain the steps for the learner

Suppose you are going to estimate 9 I/ C082$dw. 0 using the trapezoidal rule. According to the error bound, what is the minimum number of points \"min needed to guarantee that the absolute value of the error is less than 106 ? \"min : Number Consider the data: x j 0 2 3 4 of ( 20 ; ) -5 -2 2 3 4 Applying Simpson's rule to this data, the estimate of the integral I = Jo f(x) dac is I~ NumberFinite difference formulae Evaluating the derivative of the quadratic interpolant at the data points yields the finite difference formulae (Kreyszig 2011, $19.5) -fitl + 4fj - 3fi-1 2h f ~ p'2(2; ) = ... _ Jiti - fi-1 2h 3fi+1 - Afj +fi-1 2h f" ~ p'" (x;) = Ji-1 -2fit fitl h2 Taylor's theorem also derives these formulae.Let fi = f(a;), f = f'(x;), f! = f"(x;) and so on, where a; are equispaced grid points with spacing h = * j+1-aj. Applying Taylor's theorem about the point ;, f j - 2 = fj t af* +bf" + cf!" + af(iv)(t), where a = b = C = d =Use the finite-difference formulae from page 126 of the notes (print version) to find approximate values of the derivatives f; in the following table. Use the centred-difference approximation wherever possible. Enter your answers to two decimal places accuracy. f; Number Number Number I Number A certain function is differentiated numerically. Suppose we known that for this class of functions, the error is 001.6) as h % 0, where h is the grid spacing. When the grid spacing is halved, the error is usually expected to decrease by a factor of Number