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, a m , ∆a , m- .
1. ) , , . ) . ( )
2. , m . ( )
1.
a=0.124560.0005
b=0.120780.00003
c=2.080.015
) 
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, 
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d (xy)~d (x/y)<d x+d y, D (xy)<D x+D y, d (xy)<MAX(d x, d y) D f(x)~f'(x) × D x:
:
D a = 0,0005, D b = 0,00003, D c = 0,015.
:
δa=0.004014129736673, δb=0.000248385434287, δc=0.007211538461538
:
| a^4=0.00024 => | δa^4=4*δa =0.0160565 => | Δa^4=0.00024*0.0160565=0.00000385356 |
| b^4=0.00021 => | δb^4=0.0009935 => | Δb^4=0.000000208635 |
| a^4-b^4=0.00003 | Δ(a^4-b^4)= =0.000003644925 | δ(a^4-b^4)=0.1214975 |
| a*b=0.0150443568 | Δ(a*b)=0.000000015 | δ(a*b)=0.0000009970516 |
| (a*b)^2=0.00022633267 | Δ((a*b)^2)= =0,00000000045 | δ((a*b)^2)=0.00000199 |
| (a^4-b^4)/(a*b)^2= =0.13254825298 | Δ ((a^4-b^4)/(a*b)^2)= =0,016104 | δ ((a^4-b^4)/(a*b)^2)= =0,121499 |
| a+c=2.20456 | Δ(a+c)=0.0155 | δ (a+c)=0.00703088144573 |
| sin(a+c)=0.8058 | Δ(sin(a+c))=|(sin(a+c))¢| × D (a+c)= =|cos(a+c)|D (a+c)= =0.5922*0.0155=0.00918 | δ (sin(a+c))=0,0113924 |
| ln(sin(a+c))=-0.2159197 | Δ(ln(sin(a+c)))=|(ln(sin(a+c)))¢|= =|1/sin(a+c)*(sin(a+c))¢|=0.0113924 | δ (ln(sin(a+c)))=- 0.0527622 |
| F = (a^4-b^4)/(a*b)^2 *ln(sin(a+c)) = =-0.02861978 | δF=δ ((a^4-b^4)/(a*b)^2) + δ(ln(sin(a+c)))= 0.0687368 | ΔF= F*ᵟF=0.0019672 |
) D F = 0.0019672, F= -0.02861978, m =4.
, : F = -0,028 61978
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|
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2.
F= 
a = 0.02456, b=0.01823, c=0.348, m=5
:
a+b=0.04279,
a-b=0.00633,
(a-b)1/2=0.07956,
(a+b)/(a-b)1/2=0.53783,
a+c=0.37256,
sin(a+c)=0.364,
ln(sin(a+c))=-1.010599,
F=(a+b)/(a-b)1/2* ln(sin(a+c))=- 0.5435 3028 ( 5 ).
ΔF<=0.0002
1. 
F/ a = ((a-b)1/2-(a+b) / (2*(a-b)1/2)) / (a-b) * ln(sin(a+c)) + (a+b)/(a-b)1/2 * cos(a+c)/sin(a+c) = =31.607148
= 0.0002/(3*31.607148) = 0.000002109
2. F/ b = ((a-b)1/2-(a+b) / (2*(a-b)1/2)) / (a-b) = 12.299805
= 0.0002/(3*12.299805) = 0.00000542
3. F/ c = cos(a+c)/sin(a+c) = 2.55878
Δc = 0.000026054
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