ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
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ɂɡ ɜɵɪɚɠɟɧɢɹ (20), ɧɚɩɪɢɦɟɪ, ɜɢɞɧɨ, ɱɬɨ ɟɫɥɢ
( )
const,
t
O
{
ɬɨ
( ) 1.
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ɗɬɨɬ ɜɵɜɨɞ ɫɥɟɞɭɟɬ ɬɚɤɠɟ ɢɡ ɮɨɪɦɭɥɵ (18).
Ɋɚɫɫɦɨɬɪɢɦ ɤɥɚɫɫ ɨɛɴɟɤɬɨɜ, ɭ ɤɨɬɨɪɵɯ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɬɤɚɡɨɜ
( )
t
O
ɤɚɤ ɮɭɧɤɰɢɹ ɜɪɟɦɟɧɢ
t
ɦɨɧɨɬɨɧɧɨ ɪɚɫɬɟɬ. ɗɬɨɬ ɤɥɚɫɫ ɢɧɬɟɧɫɢɜ-
ɧɨ «ɫɬɚɪɟɸɳɢɯ» ɨɛɴɟɤɬɨɜ ɧɚɢɛɨɥɟɟ ɨɩɚɫɟɧ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ. ɉɨɫɤɨɥɶ-
ɤɭ ɞɥɹ ɬɚɤɢɯ ɨɛɴɟɤɬɨɜ
( ) (
),
t
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O W
ɬɨ, ɫɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (20),
( ) 1.
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W
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Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɞɥɹ ɢɧɬɟɧɫɢɜɧɨ «ɫɬɚɪɟɸɳɢɯ» ɨɛɴɟɤɬɨɜ
ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɤɚɫɚɬɟɥɶɧɨɣ ɩɪɹɦɨɣ, ɩɪɨɜɟɞɟɧɧɨɣ ɤ ɤɪɢɜɨɣ
( )
l
U W
ɜ ɥɸɛɨɣ ɬɨɱɤɟ
,
W
ɢɦɟɟɬ ɭɝɨɥ ɧɚɤɥɨɧɚ ɤ ɨɫɢ ɚɛɫɰɢɫɫ ɦɟɧɶɲɟ
ɱɟɦ
4.
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Ʉɪɨɦɟ ɬɨɝɨ, ɮɭɧɤɰɢɹ ( ),
l
U W
ɫɨɝɥɚɫɧɨ (7), ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ
( ) 0.
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W
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Ɉɬɤɭɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɮɭɧɤɰɢɹ ( )
l
U W
ɦɨɧɨɬɨɧɧɨ ɪɚɫɬɟɬ.
ȿɫɥɢ ɩɪɢɧɹɬɶ, ɱɬɨ
(
ɫ)
(
c)
lim ( ),
t
L
t
O
of
ɝɞɟ
(
c)
( )
t
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—
ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɬɤɚɡɨɜ «ɫɬɚɪɟɸɳɟɝɨ» ɨɛɴɟɤɬɚ, ɬɨ ɜ ɫɨ-
ɨɬɜɟɬɫɬɜɢɢ ɫ ɬɟɨɪɟɦɨɣ 2 ɭɪɚɜɧɟɧɢɟ ɧɚɤɥɨɧɧɨɣ ɚɫɢɦɩɬɨɬɵ ɛɭɞɟɬ
ɢɦɟɬɶ ɜɢɞ
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ɫ)
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b
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(
ɫ)
(
ɫ)
(
ɫ)
1 1
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Ɉɛɴɟɞɢɧɢɜ ɜɵɜɨɞɵ, ɫɞɟɥɚɧɧɵɟ ɞɥɹ ɢɧɬɟɧɫɢɜɧɨ «ɫɬɚɪɟɸɳɢɯ»
ɨɛɴɟɤɬɨɜ, ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɩɪɢɦɟɪɧɵɣ ɝɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɩɨɤɚɡɚɬɟɥɹ
(
c)
( )
l
U
W
ɤɚɤ ɮɭɧɤɰɢɸ ɜɪɟɦɟɧɢ
W
ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɧɚɤɥɨɧɧɭɸ
ɚɫɢɦɩɬɨɬɭ (ɪɢɫ. 1).
Ɍɨɱɧɨ ɬɚɤ ɠɟ, ɪɚɫɫɦɚɬɪɢɜɚɹ ɤɥɚɫɫ ɨɛɴɟɤɬɨɜ, ɭ ɤɨɬɨɪɵɯ ɢɧɬɟɧɫɢɜ-
ɧɨɫɬɶ ɨɬɤɚɡɨɜ, ɧɚɩɪɨɬɢɜ, ɦɨɧɨɬɨɧɧɨ ɭɛɵɜɚɟɬ (ɤɥɚɫɫ «ɦɨɥɨɞɟɸɳɢɯ»
ɌɈɈ), ɛɭɞɟɦ ɢɦɟɬɶ ( ) (
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t
O W
O W
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ɨɬɤɭɞɚ, ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ (20),
ɧɚɣɞɟɦ
( ) 1.
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W
w
!
w
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɤɚɫɚɬɟɥɶ-
ɧɨɣ ɩɪɹɦɨɣ, ɩɪɨɜɟɞɟɧɧɨɣ ɤ ɤɪɢɜɨɣ
( )
l
U W
ɜ ɥɸɛɨɣ ɬɨɱɤɟ
,
W
ɢɦɟɟɬ
ɭɝɨɥ ɧɚɤɥɨɧɚ ɤ ɨɫɢ ɚɛɫɰɢɫɫ ɛɨɥɶɲɟ ɱɟɦ
4.
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