North Maharashtra University 2008 B.Sc Mathematics S.YBSc - MTH – 222 (B) (Numerical Analysis) - Question Paper

- - - - equations can be solved for 2 unknowns a and b.
4) 1 of the normal equations for fitting the straight line y = a + bx is
provided by S i i x y = - - - -
5) 1 of the normal equations for fitting the parabola y = a + bx + cx2 is
S i i x two y = - - - -
6) The normal formula for fitting of a straight line y = a + bx is S i y =
- - - - - -
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a) na + b S i x b) n2a + b S 2
i x
c) na + b S 2
i x d) a + b S i x
7) The normal formula for fitting of a straight line y = a + bx + cx2 is
S i i x y = - - - - - -
a) S + S two + S 3
i i i a x b x c x b) S + S three + S 4
i i i a x b x c x
c) S two + S + S 3
i i i a x b x c x d) S + S three + S 2
i i i a x b x c x
8) The method of - - - - is the most systematic procedure to fit a unique
curve from provided data
a) lowest squares b) lowest cube c) square d) none of these
9) - - - -means to form an formula of the curve from the provided data
a) lowest b) square c) curve fitting d) none of these
10) From the data
x 0 one two three 4
y one 0 three 10 21
S 2
i x = - - - - -
a) 12 b) 13 c) 14 d) 6
3 : ques. of four marks
1) discuss the lowest square method for fitting a curve.
2) discuss the method of lowest squares for fitting a straight line y = a + bx to
the provided data.
3) discuss how to fit a 2nd degree polynomial y = a + bx + cx2 by using
the method of lowest squares to the provided data.
4) discuss how we fit a power function y = axb to the provided data by using
lowest square method.
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5) discuss how we fit an exponential function y = aebx to the provided data by
using the method of lowest squares.
6) Use the method of lowest squares to fit the straight line y = a + bx to the
data provided beneath
X 0 one two three 4
Y one 2.9 4.8 6.7 8.6
7) Use the method of lowest squares to fit the straight line y = a + bx to every
of the data provided beneath
i)
ii)
iii)
iv)
v)
vi)
x 0 one two 3
y two five eight 11
x one two three four six 8
y 2.4 3.1 3.5 4.2 five 6
x one two three five six eight 9
y two five seven 10 12 15 19
x one two three four five 6
y 1200 900 600 200 110 50
X 0 one two three 4
Y one 1.8 3.3 4.5 6.3
x –3 –1 one four five seven 10
y –2 –1 0 1.5 two three 4.5
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vii)
8) The temperature T (in 0c) and length l (in mm) of a heated rod is provided. If
l = a + bt obtain the best value of a and b for every data :
i)
ii)
iii)
9) The subsequent table provide temperature T (in 0c) and length l (in mm) of a
heated rod. If l = a + bt, obtain the best value of a and b by using lowest
square method
10) If the straight line y = a +bx is the best fit to the set of points (x1 , y1),
(x2 , y2), - - - - -, (xn , yn). then show that
S S S
S S
i i i
i i
x y x
x y n
x y
2 2
1
= 0 for i
= 1, 2, - - - - , n.
10) obtain the value of a, b and c so that y = a + bx + cx2 is the best fitting of
every of the data provided beneath :
x six eight 10 12 14 16 18 20 22 24
y 3.8 3.7 four 3.9 4.3 4.2 4.2 4.4 4.5 4.5
T 200 300 400 500 600 700
l 600.1 600.4 600.6 600.7 600.9 601.0
T 100 300 500 700 900 1100
l 200.1 200.3 200.5 200.7 200.9 201.1
T 200 400 600 800 1000 1200
l 100 200 300 350 400 500
T 200 300 400 500 600 700
l 800.3 800.4 800.6 800.7 800.9 801.0
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i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x 0 one two three 4
y one 0 three 10 21
x 0 one 2
y one six 17
x 0 one two 3
y one six 17 34
x 0.78 1.56 2.34 3.12 3.81
y 2.5 1.2 1.12 2.25 4.28
x 1929 1930 1931 1932 1933
y 352 356 357 358 360
x one 1.5 two 2.5 three 3.5 4
y 1.1 1.3 1.6 2.0 2.7 3.4 4.1
x one 1.5 two 2.5 three 3.5 4
y 1.1 1.2 1.5 2.6 2.8 3.3 4.1
x one two three four five six seven eight 9
y two six seven eight 10 11 11 10 9
x 0.78 1.56 2.34 3.12 3.81
y 2.5 1.2 1.12 2.25 4.28
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x)
12) Fit the power function y = axb to every of the data provided beneath :
i)
ii)
iii)
iv)
v)
vi)
13) Fit the exponential function y = aebx for every of the data provided beneath :
i)
ii)
x 0 one two 3
y one six 17 34
x one two three 4
y 60 30 20 15
x two four seven 10
y 43 25 18 13
x 2.2 2.7 3.5 4.1
y 65 60 53 50
x one two three four 5
y 15.3 20.5 27.4 36.6 49.1
x 0.5 one 1.5 two 2.5 3
y 1.62 one 0.75 0.62 0.52 0.46
x one two three four 5
y 1290 900 600 200 110
x one 1.2 1.4 1.6
y 40.17 73.196 133.372 243.02
x one two three 4
y 60 30 20 15
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iii)
iv)
v)
vi)
vii)
14) Determine the constants a and b for y = aebx for the subsequent data by lowest
squares method

Earning:   Approval pending.