Iloilo Science and Technology UniversityBurgos St., La Paz, Iloilo City

EMath 124 Numerical MethodsMIDTERM EXAMINATION August 2015

General Direction

Utilize blue book(s) in answering this examination. Other paper(s) will not be considered.

.1. [ 15 pts] Complete the table below, with reference to absolute error 0.0001.

i xi xi+1 ei Remarks

0 0.900000 1.438180 0.538180 continue1 1.438180 1.259695 0.178485 continue2 1.259695 1.163420 0.096275 continue3 1.163420 1.136582 0.026838 continue4 1.136582 1.134732 0.001849 continue5 1.134732 1.134724 0.000008 STOP!

2. [15 pts] Fill-in the missing data in the table below, with remarks in reference to relative error 0.0001.

k xk xk+1 dk Remarks0 0.000000 -1.000000 1.000000 continue1 -1.000000 -0.857143 0.166667 continue2 -0.857143 -0.789952 0.085057 continue3 -0.789952 -0.778373 0.014876 continue4 -0.778373 -0.778090 0.000364 continue5 -0.778090 -0.778090 0.000000 continue

3. [10 pts] Find and correct a misprint in this data.yk 1 3 11 31 69 113 223 351 521 739 1011

4. [10 pts] Assuming that the following yk values belong to a polynomial of degree four, compute the next three values.

k 0 1 2 3 4 5 6 7yk 0 1 2 1 0

5. [15 pts] Find all positive, nonzero roots of using the Newton-Raphson method. Show your approximation through a table with relative error less than or equal to 0.001.

6. [15 pts] In using the method of successive substitution, what will you use to determine a root of and why? Show at least 5 iterations using a table.

7. [15 pts] Find a root of that lies on the interval with error 0.001 relative. Use method of bisection or half-interval method.

8. [15 pts] Complete the table below. Compute up through fourth differences of the discrete function displayed in the xk, yk columns.

0 1 1

1 2 15

2 3 53

3 4 127

4 5 249

5 6 431

6 7 685

7 8 1023

8 9 1457

9. [10 pts] Compute the following factorials: a. b.

Prepared by: [Signed] NACI JOHN C. TRANCE, PECEAsso. Professor III

Reviewed by: [Signed] CARLITO S. ANATAN, PECEHead, ECE Department

Approved: [Signed] RUSS ALLEN B. NAPUD, DIT, ECE

Dean, College of Eng’g and Architecture