North Maharashtra University 2008 B.Sc Mathematics S.Y. - MTH – 222 (B) (Numerical Analysis) - exam paper

number - - - -
a) 32.68 b) 32.69 c) 32.67 d) 32.686
6) In bisection method if roots lies ranging from a and b then f(a)× f(b) is - - - -
a) < 0 b) = 0 c) > 0 d) none of these
7) If percentage fault of a number is 3.264×10-4 then its relative
fault is - - - -
a) 3.264×10-5 b) 3.264×10-6
c) 3.264×10-7 d) none of these
8) The root of the formula x3 – 2x – five = 0 lies ranging from - - - -
a) 0 and one b) one and two c) two and three d) three and 4
9) In Newton Raphson method for finding the real root of formula
f(x) = 0, the value of x is provided by - - - -
a) x0 -
f'(x0 )
f(x0 )
b) x0 c)
f'(x0 )
f(x0 )
d) none of these
3 : ques. of four marks
1) discuss the Bisection method for finding the real root of an formula
f(x) = 0.
2) discuss the method of false position for finding the real root of an
formula f(x) = 0.
3) discuss the iteration method for finding the real root of an formula
f(x) = 0. Also state the needed conditions.
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4) State and prove Newton-Raphson formula for finding the real root of
an formula f(x) = 0.
5) discuss in brief Inherent fault and Truncation fault. What is meant by
absolute, relative and percentage errors? discuss.
6) Using the Bisection method obtain the real root of every of the formula :
(i) x3 – x – one = 0. (ii) x3 + x2 + x + seven = 0.
(iii) x3 – 4x – nine = 0. (iv) x3 – x – four = 0.
(v) x3 – 18 = 0. (vi) x3 – x2 – one = 0.
(vii) x3 – 2x – five = 0. (viii) x3 – 9x + one = 0.
(ix) x3 – 10 = 0. (x) 8x3 – 2x – one = 0.
(xi) 3x – one + sin x = 0. (xii) xlog10x = 1.2.
(xiii) x3 – 5x + one = 0. (xiv) x3 – 16x2 + three = 0.
(xv) x3 – 20x2 – 3x + 18 = 0. (up to 3 iterations).
7) Using Newton-Raphson method, obtain the real root of every of the
equations provided bellow (up to 3 iterations) :
(i) x2 – 5x + three = 0 (ii) x4 – x – 10 = 0
(iii) x3 – x – four = 0 (iv) x3 – 2x – five = 0
(v) x5 + 5x + one = 0 (vi) sinx = one – x
(vii) tanx = 4x (viii) x4 + x2 – 80 = 0
(ix) x3 – 3x – five = 0 (x) xsinx + cosx = 0
(xi) x3 + x2 + 3x + four = 0 (xii) x2 – 5x + two = 0
(xiii) 3x = cosx + one (xiv) xlog10x – 1.2 = 0
(xv) x5 – 5x + two = 0 (xvi) x3 + 2x2 + 10x – 20 = 0
8) Using Newton-Raphson method, obtain the value of every of :
(i) 10 (ii) three 13 (iii) 17 (iv) 29 (v)3 10
9) Using Newton-Raphson method, obtain the real root of every of:
(i) e-x – sinx = 0 (ii) logx = cosx (iii) logx – x + three = 0
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10) Using the method of false position, find a real root of every of the
formula (up to three iteration)
(i) x3 + x2 + x + seven = 0 (ii) x3 – 4x – nine = 0
(iii) x3 – 18 = 0 (iv) x3 – x2 – one = 0
(v) x3 – 2x – five = 0 (vi) x3 – 9x + one = 0
(vii) x3 – x – one = 0 (viii) xlog10x – 1.2 = 0
(ix) cosx = 3x – one (x) xex = 2
(xi) x3 – x – four = 0 (xii) x3 – x2 – two = 0
(xiii) xex – three = 0 (xiv) x2 – logex – 12 = 0
11) Using the iterative method, obtain the real root of every of the formula
to 4 significant figures (up to three iterations)
(i) 2x – log10x – seven = 0 (ii) e-x = 10x
(iii) x = cosecx (iv) x = (5 – x)1/3
(v) ex = cotx (vi) 2x = cosx + 3
(vii) x3 + x2 – one = 0 (viii) cosx = 3x – 1
(ix) sinx = 10(x – 1) (x) x3 – x2 – x – one = 0
(xi) tanx = x (xii) x = 0.21sin(0.5+x)

Earning:   Approval pending.