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Sma2109:Applied Mathematics Question Paper

Sma2109:Applied Mathematics

Course:Bachelor Of Computer Science

Institution: Meru University Of Science And Technology question papers

Exam Year:2012

QUESTION ONE (30 MARKS)
a) Find the value of 2 from dx x? ? 1 0 1 1
using Euler-Maclaurin formula taking = 0.1.
(5 Marks) b) The numbers m and n when rounded off to 4s.f are 37.26 and 0.05371 respectively. Find and discuss the error involved. (4 Marks) c) Find the root of tan + = 0 up to two decimal places which lies between 2 and 2.1 by bisection method. (8 Marks) d) Evaluate 5+12 2+5+6 . (5 Marks) e) Evaluate = 2 for = 0.05 using the following table using Newton’s forward interpolation formula correct to four decimal places
0.00 0.10 0.20 0.30 0.40 = 2 1.000 1.2214 1.4918 1.8221 2.255 (8 Marks)
QUESTION TWO (20 MARKS)
a) Solve the equation tan = 1 by Regula-Falsi method starting with 2.5 and 3.0 as the initial approximations to the root. (6 Marks) b) In an examination, the number of candidates who obtained marks between certain limits were as follows Marks 30-40 40-50 50-60 60-70 70-80 No. of students 31 42 51 35 31
2
Find the number of candidates whose scores lie between 45 and 50 using Newton’s forward interpolation. (8 Marks) c) Find the value of ? ? 1 0 21 x dx Taking 5 subintervals by Trapezoidal rule, correct to five significant figures. Also compare it with its exact value. (6 Marks)
QUESTION THREE (20 MARKS)
a) Find the root of the equation sin = 1 + 3 between -2 and -1 correct to 3 decimal places by Newton – Raphson method. (8 Marks) b) Use Newton – cotes methods for = 3 to approximate the value of ? ? ? 1 0 1 x dxI , comparing your answer with the exact solution. (12 Marks)
QUESTION FOUR (20 MARKS)
a) Using Aitkens’s 2 , find the root of the equation 3 = 1 + cos. (10 Marks) b) Compute one root of 3 = 0 correct to 2d.p using Bisection method that lies between 1.5 and 1.6. (7 Marks) c) Prove that 1 + 1 = 1. (3 Marks)

Sma2109:Applied Mathematics Question Paper

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