1. Find the percentage error if 625.483 is approximated to three signicant gures.
2. Let x = 0.00458529 nd the absolute error if x is truncated to three decimal digits.
3. Let the solution of a problem be xA = 35:25 with relative error in the solution atmost 2% nd the
range of values upto 4 decimal digits, within which the exact value of the solution must lie.
4. Find the relative error in the function y = axm1
2 : : : xmn
5. Find the absolute error, relative error and percentage error of the area of triangle A =
a = 2:5 0:001 cm & b = 10:3 0:0001 cm
6. The strain in axial member of a square cross section is given by
where: F=axial force in the member in Newton, h=width of the cross section in meter, and
E=Young’s modulus in Pascal.
Given F = 6:2 0:9N; h = 4 0:1m; andE = 10 0:4pa. Find the absolute and relative errors in
the measured strain.
7. Itis required to nd the value of the function U = 6×2(log x sin 2y) to two decimal places; the
approximate value of x and y are 15:20 and 570, respectively. Find the permissible absolute error
in this quantities.
8. Find the percentage error in V (x; y) = 3x2y at x = 1 and y = 1. Given that the percentage error
in x and y are 1% and 2% respectively. Hence, by inverse method show that if the percentage error
in V is 4% then the corresponding percentage error in x and y are 1% and 2% respectively.
9. Find the relative maximum error in the function
(a) w =
u2 ifx = y = z = 1; u = 2 & x = y = z = u = 0:001
(b) F =
z4 ifx = y = z = 1; & x = y = z = 0:0001
(c) U =
ifx = y = z = 3 & x = 0:001 y = 0:002 z = 0:003
10. The value of the function u =
z3 is corrected to three decimal places & if x = y = z = 1, then
nd the permissible absolute errors in x, y & z.
11. The errors in the measurement of area of a circle is not allowed to exceed 0:5%. How accurately
should the radius be measured?
12. Using bisection method solve the following equations
(a) f(x) =
x cos x on [0, 1]. Perform only the rst three iteration
(b) x =
5 correct to two decimal place.
(c) x3 5x + 1 = 0 nd the smallest positive root correct to two decimal places.
(d) f(x) = 3x
1 + sin x correct to three decimal places.
Numerical Analysis I Math 2061
13. Using Regula Falsi method nd the smallest positive root of the equation
(a) x2 ln x 12 = 0
(b) x4 x 10 = 0,
(c) x ex = 0
14. Using Newton-Raphson method solve the following equation
(a) x4 x 10 = 0 correct to three decimal places.
(b) x sin x = 0:25 with an erorr of 0.001
(c) cos x xex = 0
15. Repeat problem # 14 using Secant method.