### Assignment I

```Babu Banarasi Das Northern India Institute of Technology, Lucknow
DEPARTMENT OF MATHEMATICS
Assignment : I Course: B.Tech Subject: CBNST Paper Code: NCS – 303 Session: 2014 -15
1. Find a real root of the equation using iteration method.
a) cosx=3x-1 correct up to four decimal places.
b) x3+x2-1=0 up to 6th iteration.
c) xex=1 between 0 and 1upto 10th iteration.
d) Evaluate the square root of 5 using iteration method by considering the following relation
x=
5
, x = x2 + x − 5,
x
2x =
5
+ x , which of
x
the following case is suitable.
1
3
2. Find the positive value of (17) correct up to four decimal place by Newton raphson method.
3. i) using Newton Raphson method to find a real root of x sin x + cos x = 0 use x= correct up to
3 decimal place.
ii)using Newton’s method find a real root between 0&1 of x 3 = 6 x − 4 correct to 5 decimal
places.
4. Find a rate of convergence of newton method & Secant method.
5. Evaluate the sum S = 3 + 5 + 7 to 4 significant digits & find its absolute and relative
errors.
6. i) If r = 3h(h − 2) find the percentage errors in r at h=1, if percentage errors in h is 5.
6
ii) if u =
7. i)
4x 2 y 3
& error in x,y,z be 0.001, compute the relative max. error in u when x=y=z=1.
z4
29 = 5.385 & 11 = 3.317 correct to 4 significant digit. Find the relative error in these
sum & difference.
ii) Multiply the following floating point numbers.
a) .1111 E 51 and .4444 E 50
b) .1234 E -49 and .1111 E -54
8. i) Find the round off error in storing the number 752.6836 using a four digit mantissa.
ii) Three approximate values of number 1/3 are given as 0.30, 0.33, 0.34 which of these three
is the best approximation.
9. Find a real root of the equation x 4 − 3x 3 + 3 x 2 − 3 x + 2 = 0 by using Birge Vieta method
,starting with p 0 = 0.5
10. Find a quadratic factor of the polynomial x 4 + 5 x 3 + 3x 2 − 5 x − 9 = 0 starting with
p 0 = 3 & q 0 = −5 by using Bairstow method. Also find a pair of root.
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