Sample TEST 1 For Students
Sample TEST 1 For Students
Sample TEST 1 For Students
(a) You have been given a task to measure the lengths of a beam and a rivet and come up
with 198.5 and 6.5 cm, respectively. If the true values are 200 and 8 cm, respectively,
compute the true error and the true percent relative error for each case. From the result
obtained, comment on which error is greater and justify your answer.
CO2/PO1/C3 (2 marks)
(b) Sketch the graph of f(x) vs. x to illustrate forward (FDM), backward (BDM) and centered
(CDM) of finite-divided-difference approximations of the first derivative with the plots of
approximation and true derivative
CO2/PO1/C3 (3 marks)
𝑥𝑥 2 𝑥𝑥 3 𝑥𝑥 4 𝑥𝑥 𝑛𝑛
𝑒𝑒 𝑥𝑥 = 1 + 𝑥𝑥 + + + + ⋯+
2! 3! 4! 𝑛𝑛!
Use the Taylor series to estimate f (x) = e –x at xi+1 = 1 with a base value of xi = 0.2.
Employ the zero-, first-, second-, and third-order versions and compute the percent
relative true error, ɛt and percent relative approximate error, ɛa for each case.
(a) Compute the root of the Equation below using Newton-Raphson method with 3 iterations
using an initial guess of 6.
(b) Check whether the Equation in (a) can be evaluated using Fixed-point (or one-point)
iteration method for the interval [5, 6] using 2 different equation arrangements. Comment
on your findings.
(c) Compare the characteristics, convergence criteria and stability between Bisection Method
and Newton-Raphson method.
CO1/PO1/C2 (5 Marks)
QUESTION 3