Find derivatives x'(t) and y'(t) algebraically. 2. Write a MATLAB function that calculate derivatives x'(t) and y'(t) numerically with the central finite differences of the second order on the mesh with spacing delta t = 2 pi/100. 3. Plot numerical x'(t) and y'(t) along with accurate values of the same derivatives. 4. Write a MATLAB function implementing the integrand and calculate the integral with the trapezoidal rule on a mesh with spacing delta x = (b - a)/(N - 1) = 0.01. The length of a curve given by a parametric equation x(t), y() is given by: integral^b_a squareroot [x'(t)]^2 + [y'(t)]^2 dt The cycloid curve is given by x = R(t - sint), and y = R(1 - cos t). Determine the length of a cycloid with R = 8 in. for 0 lessthanorequalto t lessthanorequalto 2 pi