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.1. n x0.
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.3.1.
n xi(i= 1, 2,..., n)
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. , x0, 0 ,
n. x 0 n , x x0,
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x x + dx f(x)dx. , x1x2 x x1x2(. .3).
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68,3 %>> >> >> 95,4 %>> >> >> 99,8 %
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10 ( ) 400
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x = 969,7 0,7 mm (7 ).
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I,
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2 972,3 2,61 6,81
3 970,5 0,81 0,66
4 969,0 -0,69 0,48
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S= r2, dS= 2rdr () , dS, , dr,
. dr r, r/r
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d du, d, d, . .
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. ()
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1. r= 9,73 0,01 m.
= 2r = 2r= 29,73 =
61,135 m = 2r= 20,01 = 0,06 m. = (61,14 0,06) m.
S= r2 S = 9,732= 297,42 m2.
S S = ( S/ r)r = 2 rr. S = 29,730,01 = 0,6 m2.
,S= 297,4 0,6 m2.
2.
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() ()
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3.
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III.
1 2 3 4
2 15 100 2400
0,3 0,18 0,243 0,8900
0,004 0,020 0,00140 0,03051
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1432 ~ 1430 .,
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.4.1.2.
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>> n=200 >> 5 %
>> n=5000 >> 1 %
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IV.
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4. . .
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x y, .
9. .
dy/dx=. , , (x, y) (x, y)
xy.
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.
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x y
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xy.
n (xi, yi) . .10.
xy
y=+x (.19)
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(0,a) y
. , xi
(.19) yi .
xi , y
(.19) a+xi. , yi. (xi,
yi)
. .10.
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a
di .
S
a:
T a a .
a di= yia xi
[d2]. :
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.
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V, y = a + x.
V
y = a + x
( )
xi yi xiyi xi2 di di
2
0,0 4,6 0,0 0,0 -0,04 0,0016
1,0 7,1 7,1 1,0 0,14 0,0196
2,0 9,5 19,0 4,0 0,22 0,0484
3,0 11,5 34,5 9,0 -0,10 0,0100
4,0 13,7 54,8 16,0 -0,22 0,0484
5,0 15,9 79,5 25,0 -0,34 0,1156
6,0 18,6 111,6 36,0 0,04 0,0016
7,0 20,9 146,3 49,0 0,02 0,0004
8,0 23,5 188,0 64,0 0,30 0,09009,0 25,4 228,6 81,0 -0,12 0,0144
45,0=[x] 150,7=[y] 869,4=[xy] 285,0=[x ] 0,3500=[d]
n=10
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.7. a y= a +x.
a , (yi, xi).
:
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50% .
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a (. . .11):
1.
. y= a1+1x
y 1 a1,
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2.
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a a
y= a+x. .11.
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.
x= 0 x= 13. :
: (x= 0 y= l,7) (x= 13,0 y= 10,3)
1: (x= 0 y= 2,2) (x= 13,0 y= 9,6)
2: (x= 0 y= 1,2) (x= 13,0 y= 10,7)
.
y :
a= 1,7, a1= 2,2, a2=1,2
.12. , ,
(.30),
,
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n x xi(i=1,2,n), :
(.33) x (1) .
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a , , , a , ( .6)
( .7).
1. J. Topping.Errors of Observation and their treatment. (Institute of Physics, London).
2. G.L. Squires.Practical Physics. (McGraw-Hill, U.K.).
3. P.R. Bevington.Data Reduction and Error Analysis for the Physical Sciences.
(McGraw-Hill, N.Y.).
4. H. Young. Statistical Treatment of Experimental Data. (McGraw - Hill, N.Y.).
5. N.C. Barford.Experimental Measurements: Precision, Error and Truth. (Addison
Wesley, Reading, Mass.).6. S.L. Meyer.Data Analysis for Scientists and Engineers. (J. Wiley and sons, N.Y.).