only 3.5 , 3.7 and 3.8

Exercise 3.5 Use Adaptive Quadrature (Adaptive Trapezoidal and Simpson's Rules) to approximate the integral with TOL=0.005 [, ( + sin(e * )dx. Exercise 3.6 Taylor's theorem can be used to show that centred-difference formula 'Three-Point Midpoint Formula' f (x0 ) = =[f(xoth) - f(xoth)] -- 103)(5), EE (x0 - h, xoth). to approximate f'(xo) can be expressed with an error formula f' (xo) = = [f(xo + h) - f(xo+ h)]- - f(3) (xo ) - 120' f(5) ( x0 ) -.... Find approximation of order O(h2), O(h4), and O(h6) for f'(2.0) when f(x) = xet and h = 0.2. 78 3 Numerical Integration Exercise 3.7 Apply Romberg Integration to approximate S, log(x)dx (iterate to j = 3 in Algorithm 7). Exercise 3.8 Approximate S edx and f, In(x)dx by using Gaussian-Legendre quadrature with n = 3