(iv) (4 marks) Finally, compute the error of your interpolated value compared to the actual value of sinh(1.5). What if you were to interpolate at it: = 0.5? Would you expect your polynomial to be a reasonable approximation at this point? Explain your reasoning in words. QUESTION 5 (15 MARKS): The hyperbolic sine function is an elementary transcendental function made out of a difference of exponentials as follows: (93 e'\" sinhr) = 2 (5) In this question you will be tting a quadratic interpolation function to it, in the interval 0 g m In-1,i(x)yi i=0 where the basis functions are: n-1 In-1,j (2) = II C - Ci i-0,i/j Cj - Ci Gaussian Quadrature ( f(x) da ~ [wif(Ii) # terms values of ri weight wi 2 -0.57735027 1.0 +0.57735027 1.0 -0.77459667 0.5555555 0.0 0.8888888 +0.77459667 0.5555555 Finite-difference formulas f'(20) = JI - fo h " + O(h) (forward) f'(xo) = fo - J-1 + O(h) (backward) h f'(20) = f1 - f-1 + 0(h2) (central) 2h f"(20) = f2 - 2f1+ fo + O(h) h2 f"(20) = f1 - 2fo + f-1 + 0(h2) h2 Gauss-Seidel Method :-1 n-1 k+1 Caijack , 0 siEn ari -0 j=i+1