Mathematics Questions (Need No Plagurism)

1. What is the nth order approximation using Taylor series? (10 points)
2. What is Error Propagation? (10 points)
3. Please explain what the total numerical error is? Please illustrate how the change of step size will affect the total numerical error? (20 points)
4. What are non-computer methods for determining roots? (10 points)
5. Please illustrate with an example about graphical methods to obtain roots. (10 points)
6. Please illustrate the bisection method to obtain roots. (10 points)
7. Determine the real roots of f(x)=-0.5×2+2.5x+ 4.5 
(a) Graphically (10 points)
(b) Using the quadratic formula (10 points)
(c) Using three iterations of the bisection method to determine the highest root. Employ initial guesses of xl=5 and xu=10. Compute the estimated error ɛa and the true error ɛt after each iteration.