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 proble

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

1 xm2

2 : : : xmn

n .

5. Find the absolute error, relative error and percentage error of the area of triangle A =

1

2

ab if

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

” =

F

h2E

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 =

6xy3z5

u2 ifx = y = z = 1; u = 2 & x = y = z = u = 0:001

(b) F =

4x2y3

z4 ifx = y = z = 1; & x = y = z = 0:0001

(c) U =

x2y

z

ifx = y = z = 3 & x = 0:001 y = 0:002 z = 0:003

10. The value of the function u =

5xy2

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) =

p

x cos x on [0, 1]. Perform only the rst three iteration

(b) x =

p

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

p

1 + sin x correct to three decimal places.

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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.

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