Numerical Analysis

Daffodil International University Faculty of Science & Information Technology Department of Software Engineering Midterm Examination, Summer 2026 Course Code: Numerical Analysis; Course Title: SE341 Sections & Teachers: A, B, C, D (RT), E(TR) Time: 1 Hour 30 Mins Marks: 25 Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. All portions of each question must be answered sequentially.] 1. a) A student measures the density of a material as 49.996 g/cm^3, while the accepted value is 50.000 g/cm^3. Round the measured value to four significant digits and compute the absolute error, relative error, and percentage error. [Marks-3] CLO-1 Level-2 1. b) Describe the concept of accuracy and precision. [Marks-3] 1. c) A city planner develops a linear mathematical model to predict the population growth of a city, although the actual growth pattern is nonlinear. During the computation, the value of pi is approximated as 3.1416 instead of its full value. The population data used in the model are collected using a sensor with a tolerance of +-0.5%, and while entering the data into the computer, an operator mistakenly records 25,000 as 2,500. Explain the type of error associated with each of the four situations. [Marks-4] 2. a) Identify the root of the given equation f(x) = x^3 - 4x - 9 = 0 using the Bisection Method when the true value is 2.7065 and stopping criteria is absolute error should be less than 0.0007. Additionally, explain the algorithm for the Bisection Method. [Marks-7] CLO-2 Level-4 2. b) Examine the root of the equation f(x) = sinx + 2x^2 - 4 = 0 using the False Position method to find the root, rounding your result to five decimal places (8th iteration). Additionally, illustrate the merits and demerits of the False Position Method. [Marks-8]