Экономика (с ответами). Всероссийская олимпиада школьников в Москве (2021-2009 год) - часть 94

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 ʀʖʠ ʦʖʧʥʦʛʚʛʡʵʨʲ ʥʦʤʞʝʘʛʚʛʣʣʱʟ ʘʱʥʩʧʠ ʢʛʜʚʩ ʦʱʣʠʖʢʞ 
 ʇʠʤʡʲʠʤ ʘʧʛʙʤ ʥʦʤʞʝʘʤʚʞʨʲ 
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ʠʖʫ ɺʛʟʧʨʘʞʨʛʡʲʣʤ ʠʖʜʚʩʴ ʛʚʞʣʞʬʩ ʨʤʘʖʦʖ ʣʩʜʣʤ ʥʦʤʚʖʘʖʨʲ ʨʖʢ ʙʚʛ ʤʣʖ ʧʞʡʲʣʛʛ ʩʘʛʡʞʭʞʘʖʛʨ
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ʨʤʙʤ ʗʩʚʛʨ ʡʞ ʪʞʦʢʖ ʘʱʫʤʚʞʨʲ ʣʖ ʘʣʛʮʣʞʟ ʦʱʣʤʠ ʤʧʩʯʛʧʨʘʡʵʵ ʥʦʤʞʝʘʤʚʧʨʘʤ ʥʦʤʚʩʠʬʞʞ ʨʤʡʲ
ʠʤ ʣʖ ʤʚʣʤʢ ʞʡʞ ʤʚʣʤʘʦʛʢʛʣʣʤ ʣʖ ʚʘʩʫ ʝʖʘʤʚʖʫ ɾʨʖʠ ʪʞʦʢʖ ʥʤʡʩʭʞʨ ʣʖ ʘʣʩʨʦʛʣʣʛʢ ʦʱʣʠʛ
ʘʱʦʩʭʠʩ ʦʖʘʣʩʴ 

 ʖʥʦʛʡʵ  ʙ

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ʄʨʘʛʨʞʨʲ ʣʖ ʘʨʤʦʤʟ ʘʤʥʦʤʧ ʢʤʜʣʤ ʥʦʞʦʖʘʣʵʘ ʥʦʛʚʛʡʲʣʩʴ ʘʱʦʩʭʠʩ ʦʖʘʣʩʴ ʬʛʣʛ ʘʣʛʮʣʛʙʤ

ʦʱʣʠʖ ʠ ʤʗʯʞʢ ʥʦʛʚʛʡʲʣʱʢ ʞʝʚʛʦʜʠʖʢ ʅʤʧʠʤʡʲʠʩ ʥʦʛʚʛʡʲʣʱʛ ʞʝʚʛʦʜʠʞ  ʠʖʠ ʘ ʧʡʩʭʖʛ ʤʚʣʤ
ʙʤ ʨʖʠ ʞ ʘ ʧʡʩʭʖʛ ʚʘʩʫ ʝʖʘʤʚʤʘ ʘʤʝʦʖʧʨʖʴʨ ʣʩʜʣʤ ʥʦʤʚʖʘʖʨʲ ʨʤʘʖʦ ʥʤʠʖ ʥʦʛʚʛʡʲʣʱʟ ʚʤʫʤʚ ʞʫ
ʥʦʛʘʱʮʖʛʨ ʨʤ ʛʧʨʲ ʥʤʠʖ ʥʦʞʗʱʡʲ ʩʘʛʡʞʭʞʘʖʛʨʧʵ ʅʤʡʩʭʖʛʢ

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ʇʫʛʢʖ ʤʬʛʣʞʘʖʣʞʵ

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ʚʤ  ʗʖʡʡʤʘ

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ʝʖ ʤʨʧʩʨʧʨʘʞʛ ʤʗʤʧʣʤʘʖʣʞʵ ʢʖʠʧʞʢʩʢʖ ʚʡʵ ʥʖʦʖʗʤʡʱ

•

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 ʗʖʡʡ

ʝʖ ʠʖʜʚʩʴ ɻʧʡʞ ʤʮʞʗʠʖ ʧʩʯʛʧʨʘʛʣʣʖ ʤʗʣʩʡʵʡʞʧʲ ʗʖʡ

ʡʱ ʝʖ ʨʛ ʥʩʣʠʨʱ ʣʖ ʠʤʨʤʦʱʛ ʤʣʖ ʢʤʙʡʖ ʥʤʘʡʞʵʨʲ ʚʖʜʛ ʛʧʡʞ ʘʱʘʤʚʱ ʗʱʡʞ ʥʦʖʘʞʡʲʣʱʢʞ

ʖ

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ʦʖʧʭʶʨ ʥʦʞʗʱʡʞ ʚʡʵ ʤʚʣʤʙʤ ʝʖʘʤʚʖ oo

 ʗʖʡʡʖ

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

•

ʤʗʤʧʣʤʘʖʣʞʛ ʨʤʙʤ ʭʨʤ ʚʡʵ ʚʘʩʫ ʝʖʘʤʚʤʘ ʤʗʰʛʢʱ ʥʦʤʞʝʘʤʚʧʨʘʖ ʣʖ ʣʞʫ ʗʩʚʩʨ ʤʚʞʣʖʠʤʘʱ oo

 ʗʖʡʡʖ

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ʦʖʧʭʶʨ ʥʦʞʗʱʡʞ ʚʡʵ ʚʘʩʫ ʝʖʘʤʚʤʘ oo

 ʗʖʡʡʖ

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ʘʱʘʤʚ ʤ ʣʛʬʛʡʛʧʤʤʗʦʖʝʣʤʧʨʞ ʤʨʠʦʱʨʞʵ ʘʨʤʦʤʙʤ ʝʖʘʤʚʖ oo

 ʗʖʡʡ

ʗ

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ʣʤʠ oo

 ʗʖʡʡʤʘ

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ʤʥʦʛʚʛʡʛʣʞʛ ʤʗʰʛʢʖ ʥʦʤʚʖʜ ʚʡʵ ʘʣʩʨʦʛʣʣʛʙʤ ʦʱʣʠʖ oo

 ʗʖʡʡʤʘ

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ʦʖʧʭʶʨ ʥʦʞʗʱʡʞ ʚʡʵ ʤʚʣʤʙʤ ʝʖʘʤʚʖ oo

 ʗʖʡʡʖ

•

ʦʖʧʭʶʨ ʥʦʞʗʱʡʞ ʚʡʵ ʚʘʩʫ ʝʖʘʤʚʤʘ oo

 ʗʖʡʡʤʘ

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ʘʱʘʤʚ ʤ ʬʛʡʛʧʤʤʗʦʖʝʣʤʧʨʞ ʤʨʠʦʱʨʞʵ ʚʘʩʫ ʝʖʘʤʚʤʘ oo

 ʗʖʡʡʖ

ɶʡʲʨʛʦʣʖʨʞʘʣʱʛ ʠʦʞʨʛʦʞʞ ʚʡʵ ʥʩʣʠʨʖ

ʗ

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ʥʤʧʨʦʤʛʣʞʛ ʪʩʣʠʬʞʞ ʥʦʞʗʱʡʞ ʚʡʵ ʤʚʣʤʙʤ ʝʖʘʤʚʖ ʦʖʗʤʨʖʴʯʛʙʤ ʣʖ ʚʘʩʫ ʦʱʣʠʖʫ ʤʥʦʛʚʛʡʛ
ʣʞʛ ʤʥʨʞʢʖʡʲʣʤʙʤ ʤʗʰʶʢʖ ʥʦʤʞʝʘʤʚʧʨʘʖ ʞ ʥʦʞʗʱʡʞ oo

 ʗʖʡʡʤʘ

•

ʥʤʧʨʦʤʛʣʞʛ ʪʩʣʠʬʞʞ ʥʦʞʗʱʡʞ ʚʡʵ ʚʘʩʫ ʝʖʘʤʚʤʘ ʦʖʗʤʨʖʴʯʞʫ ʣʖ ʚʘʩʫ ʦʱʣʠʖʫ ʤʥʦʛʚʛʡʛʣʞʛ
ʤʥʨʞʢʖʡʲʣʤʙʤ ʤʗʰʶʢʖ ʥʦʤʞʝʘʤʚʧʨʘʖ ʞ ʥʦʞʗʱʡʞ oo

 ʗʖʡʡʤʘ

•

ʘʱʘʤʚ ʤ ʬʛʡʛʧʤʤʗʦʖʝʣʤʧʨʞ ʳʠʧʥʤʦʨʖ oo

 ʗʖʡʡʖ

•

ʘʱʘʤʚ ʤ ʬʛʡʛʧʤʤʗʦʖʝʣʤʧʨʞ ʤʨʠʦʱʨʞʵ ʚʘʩʫ ʝʖʘʤʚʤʘ oo

 ʗʖʡʡʖ

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

ɽʖʚʖʭʖ 

 ɸ ʭʶʢ ʧʤʙʡʖʧʣʱ ʳʠʤʣʤʢʞʧʨʱ

ɾʧʧʡʛʚʤʘʖʨʛʡʞ ɺʳʣ ʊʩʡʡʛʦ ʞ ɺʤʦʞʧ ɹʛʟʚʛʇʨʛʘʛʣʧʤʣ ʥʦʤʖʣʖʡʞʝʞʦʤʘʖʡʞ ʦʛʝʩʡʲʨʖʨʱ ʤʥʦʤʧʖ

ʤ ʠʡʴʭʛʘʱʫ ʥʦʤʗʡʛʢʖʫ ʳʠʤʣʤʢʞʭʛʧʠʤʟ ʥʤʡʞʨʞʠʞ ʥʦʤʘʛʚʛʣʣʤʙʤ ʘ  ʙʤʚʩ ʧʦʛʚʞ  ʥʦʤʪʛʧ
ʧʞʤʣʖʡʲʣʱʫ ʖʢʛʦʞʠʖʣʧʠʞʫ ʳʠʤʣʤʢʞʧʨʤʘ

ʇʦʛʚʞ ʦʛʧʥʤʣʚʛʣʨʤʘ ʗʱʡʞ ʠʖʠ ʥʦʛʚʧʨʖʘʞʨʛʡʞ ʖʠʖʚʛ

ʢʞʭʛʧʠʤʙʤ ʧʤʤʗʯʛʧʨʘʖ ʨʖʠ ʞ ʳʠʤʣʤʢʞʧʨʱ ʦʖʗʤʨʖʴʯʞʛ ʣʖ ʙʤʧʩʚʖʦʧʨʘʤ ʖ ʨʖʠʜʛ ʥʦʛʚʧʨʖʘʞʨʛʡʞ
ʗʞʝʣʛʧʖ ʀʖʜʚʤʢʩ ʞʝ ʣʞʫ ʥʦʛʚʡʖʙʖʡʤʧʲ ʘʱʧʠʖʝʖʨʲ ʧʘʤʛ ʤʨʣʤʮʛʣʞʛ ʠ  ʩʨʘʛʦʜʚʛʣʞʵʢ ʘ ʬʛʡʤʢ
ʧʤʙʡʖʧʞʨʲʧʵ ʧʤʙʡʖʧʞʨʲʧʵ ʥʦʞ ʤʥʦʛʚʛʡʛʣʣʱʫ ʤʙʤʘʤʦʠʖʫ ʞʡʞ ʘʱʦʖʝʞʨʲ ʣʛʧʤʙʡʖʧʞʛ

ʃʞʜʛ ʥʦʞʘʤʚʵʨʧʵ ʚʘʖ ʩʨʘʛʦʜʚʛʣʞʵ ʧ ʠʤʨʤʦʱʢʞ ʤʠʖʝʖʡʞʧʲ ʘ ʨʤʟ ʞʡʞ ʞʣʤʟ ʧʨʛʥʛʣʞ ʧʤʙʡʖʧʣʱ

ʗʤʡʲʮʛ ʘʧʛʙʤ ʤʥʦʤʮʛʣʣʱʫ  ɸ ʧʠʤʗʠʖʫ ʩʠʖʝʖʣʖ ʚʤʡʵ ʤʥʦʤʮʛʣʣʱʫ ʘʱʦʖʝʞʘʮʞʫ ʥʤʡʣʤʛ ʧʤʙʡʖʧʞʛ
ʞ ʧʤʙʡʖʧʞʛ ʧ ʤʙʤʘʤʦʠʖʢʞ ʧʤʤʨʘʛʨʧʨʘʛʣʣʤ ʅʦʤʠʤʢʢʛʣʨʞʦʩʟʨʛ ʠʖʜʚʤʛ ʞʝ ʳʨʞʫ ʩʨʘʛʦʜʚʛʣʞʟ ʤʗʰ
ʵʧʣʞʨʛ ʥʤʭʛʢʩ ʢʣʤʙʞʢ ʳʠʤʣʤʢʞʧʨʖʢ ʤʣʤ ʠʖʜʛʨʧʵ ʧʥʦʖʘʛʚʡʞʘʱʢ ʖ ʨʖʠʜʛ ʥʤʭʛʢʩ ʨʛʢ ʣʛ ʢʛʣʛʛ
ʣʛ ʘʧʛ ʧʤʙʡʖʧʣʱ ʧ ʣʞʢ ʗʛʝʤʙʤʘʤʦʤʭʣʤ ɷʩʚʲʨʛ ʡʖʠʤʣʞʭʣʱ ʤʨʘʛʨ ʤʨʣʤʧʞʨʛʡʲʣʤ ʠʖʜʚʤʙʤ ʩʨʘʛʦʜʚʛ
ʣʞʵ ʢʤʜʛʨ ʩʢʛʧʨʞʨʲʧʵ ʘ ‰ ʥʦʛʚʡʤʜʛʣʞʟ

ʖ   ʗʖʡʡʤʘ

ɹʞʗʠʞʛ ʞ ʥʡʖʘʖʴʯʞʛ ʘʖʡʴʨʣʱʛ ʠʩʦʧʱ ʥʤʢʤʙʖʴʨ ʳʪʪʛʠʨʞʘʣʤ ʦʛʙʩʡʞʦʤʘʖʨʲ

ʢʛʜʚʩʣʖʦʤʚʣʩʴ ʘʖʡʴʨʣʩʴ ʧʞʧʨʛʢʩ

     

ʗ   ʗʖʡʡʤʘ

ɻʧʡʞ ʥʦʖʘʞʨʛʡʲʧʨʘʤ ʫʤʭʛʨ ʧʗʖʡʖʣʧʞʦʤʘʖʨʲ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʟ ʗʴʚʜʛʨ ʨʤ

ʡʩʭʮʛ ʧʤʗʡʴʚʖʨʲ ʗʖʡʖʣʧ ʣʖ ʥʦʤʨʵʜʛʣʞʞ ʳʠʤʣʤʢʞʭʛʧʠʤʙʤ ʬʞʠʡʖ ʖ ʣʛ ʠʖʜʚʱʟ ʙʤʚ

     

ʆʛʮʛʣʞʛ

ʖ ɸʤʝʢʤʜʣʱʛ ʖʦʙʩʢʛʣʨʱ ʘ ʥʤʡʲʝʩ ʩʨʘʛʦʜʚʛʣʞʵ

•

ʊʞʣʖʣʧʤʘʖʵ ʧʨʖʗʞʡʲʣʤʧʨʲ

ʅʤʚʚʛʦʜʖʣʞʛ ʪʞʠʧʞʦʤʘʖʣʣʤʙʤ ʘʖʡʴʨʣʤʙʤ ʠʩʦʧʖ ʝʖʭʖʧʨʩʴ ʨʦʛ

ʗʩʛʨ ʤʨ ʧʨʦʖʣʱ ʧʩʯʛʧʨʘʛʣʣʱʫ ʘʖʡʴʨʣʱʫ ʦʛʝʛʦʘʤʘ ʭʨʤ ʤʨʘʡʛʠʖʛʨ ʦʛʧʩʦʧʱ ʤʨ ʚʦʩʙʞʫ ʬʛʡʛʟ
ɻʧʡʞ ʦʛʝʛʦʘʱ ʗʩʚʩʨ ʞʧʭʛʦʥʖʣʱ  ʣʖʥʦʞʢʛʦ ʞʝʝʖ ʧʥʛʠʩʡʵʨʞʘʣʱʫ ʖʨʖʠ ʨʤ ʌɷ ʗʩʚʛʨ ʘʱʣʩʜ
ʚʛʣ ʤʧʩʯʛʧʨʘʞʨʲ ʚʛʘʖʡʲʘʖʬʞʴ ʣʖʬʞʤʣʖʡʲʣʤʟ ʘʖʡʴʨʱ ʠʤʨʤʦʖʵ ʘ ʨʖʠʞʫ ʩʧʡʤʘʞʵʫ ʭʖʧʨʤ ʤʠʖ
ʝʱʘʖʛʨʧʵ ʤʭʛʣʲ ʦʛʝʠʤʟ ʭʨʤ ʧʖʢʤ ʥʤ ʧʛʗʛ ʧʠʖʝʱʘʖʛʨʧʵ ʣʖ ʳʠʤʣʤʢʞʠʛ ʫʩʜʛ ʭʛʢ ʗʤʡʛʛ ʥʡʖʘ
ʣʤʛ ʥʦʞʧʥʤʧʤʗʡʛʣʞʛ ʘ ʩʧʡʤʘʞʵʫ ʥʡʖʘʖʴʯʞʫ ʠʩʦʧʤʘ

•

ʈʤʦʙʤʘʱʟ ʗʖʡʖʣʧ

ɹʞʗʠʞʛ ʘʖʡʴʨʣʱʛ ʠʩʦʧʱ ʧʥʤʧʤʗʧʨʘʩʴʨ ʩʧʨʖʣʤʘʡʛʣʞʴ ʦʖʘʣʤʘʛʧʣʤʙʤ ʨʤʦ

ʙʤʘʤʙʤ ʗʖʡʖʣʧʖ ɻʧʡʞ ʘ ʠʖʠʤʟʨʤ ʧʨʦʖʣʛ ʘʤʝʣʞʠʖʛʨ ʚʛʪʞʬʞʨ ʨʤʦʙʤʘʤʙʤ ʗʖʡʖʣʧʖ  ʥʦʛʘʱʮʛʣʞʛ
ʞʢʥʤʦʨʖ ʣʖʚ ʳʠʧʥʤʦʨʤʢ ʨʤ ʛʧʨʲ ʧʥʦʤʧ ʣʖ ʛʶ ʥʦʤʚʩʠʬʞʴ ʧʨʖʣʤʘʞʨʧʵ ʢʖʡ ʨʤ ʧʥʦʤʧ ʣʖ ʛʶ ʣʖ
ʬʞʤʣʖʡʲʣʩʴ ʘʖʡʴʨʩ ʨʖʠʜʛ ʩʢʛʣʲʮʞʨʧʵ ʘ ʦʛʝʩʡʲʨʖʨʛ ʦʖʘʣʤʘʛʧʣʱʟ ʘʖʡʴʨʣʱʟ ʠʩʦʧ ʩʥʖʚʛʨ
ʨʤʘʖʦʱ ʳʨʤʟ ʧʨʦʖʣʱ ʥʤʚʛʮʛʘʛʴʨ ʤʨʣʤʧʞʨʛʡʲʣʤ ʞʣʤʧʨʦʖʣʣʱʫ ʭʨʤ ʥʦʞʘʛʚʛʨ ʠ ʦʤʧʨʩ ʘʛʡʞʭʞ
ʣʱ ʳʠʧʥʤʦʨʖ ʞ ʧʣʞʜʛʣʞʴ ʘʛʡʞʭʞʣʱ ʞʢʥʤʦʨʖ

•

ʇʖʢʤʧʨʤʵʨʛʡʲʣʖʵ ʢʤʣʛʨʖʦʣʖʵ ʥʤʡʞʨʞʠʖ

ɸ ʩʧʡʤʘʞʵʫ ʙʞʗʠʞʫ ʘʖʡʴʨʣʱʫ ʠʩʦʧʤʘ ʬʛʣʨʦʖʡʲ

ʣʱʛ ʗʖʣʠʞ ʢʤʙʩʨ ʥʦʤʘʤʚʞʨʲ ʧʖʢʤʧʨʤʵʨʛʡʲʣʩʴ ʢʤʣʛʨʖʦʣʩʴ ʥʤʡʞʨʞʠʩ  ʣʖʥʦʞʢʛʦ ʨʖʦʙʛʨʞ
ʦʤʘʖʨʲ ʞʣʪʡʵʬʞʴ ʞ ʡʩʭʮʛ ʧʨʖʗʞʡʞʝʞʦʤʘʖʨʲ ʳʠʤʣʤʢʞʠʩ ʘ ʤʨʘʛʨ ʣʖ ʘʣʩʨʦʛʣʣʞʛ ʮʤʠʞ

ɸʤʝʢʤʜʣʱʛ ʖʦʙʩʢʛʣʨʱ ʥʦʤʨʞʘ ʩʨʘʛʦʜʚʛʣʞʵ

'VMMFS %BO BOE %PSJT (FJEF4UFWFOTPO w$POTFOTVT "NPOH &DPOPNJTUT‰"O 6QEBUFi

5IF +PVSOBM PG &DPOPNJD

&EVDBUJPO

   

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

•

ɷʤʦʲʗʖ ʧ ʞʣʪʡʵʬʞʛʟ

ɸ ʦʖʝʘʞʘʖʴʯʞʫʧʵ ʧʨʦʖʣʖʫ ʥʦʞʘʵʝʠʖ ʠʩʦʧʖ ʣʖʬʞʤʣʖʡʲʣʤʟ ʘʖʡʴʨʱ ʠ

ʘʖʡʴʨʛ ʧʨʦʖʣʱ ʧ ʣʞʝʠʤʟ ʞ ʧʨʖʗʞʡʲʣʤʟ ʞʣʪʡʵʬʞʛʟ ʢʤʜʛʨ ʗʱʨʲ ʫʤʦʤʮʞʢ ʞʣʧʨʦʩʢʛʣʨʤʢ ʚʡʵ
ʧʣʞʜʛʣʞʵ ʘʣʩʨʦʛʣʣʛʟ ʞʣʪʡʵʬʞʞ

•

ʇʨʖʗʞʡʲʣʤʧʨʲ ʤʨʣʤʧʞʨʛʡʲʣʱʫ ʬʛʣ

ɻʧʡʞ ʦʛʝʛʦʘʱ ʌɷ ʚʤʧʨʖʨʤʭʣʤ ʘʛʡʞʠʞ ʨʤ ʪʞʠʧʞʦʤʘʖʣ

ʣʱʟ ʠʩʦʧ ʢʤʜʛʨ ʧʣʞʜʖʨʲ ʞʝʢʛʣʭʞʘʤʧʨʲ ʤʨʣʤʧʞʨʛʡʲʣʱʫ ʬʛʣ ʞʢʥʤʦʨʞʦʩʛʢʱʫ ʞ ʳʠʧʥʤʦʨʞʦʩ
ʛʢʱʫ ʨʤʘʖʦʤʘ ʨʤ ʛʧʨʲ ʧʣʞʜʖʨʲ ʩʦʤʘʛʣʲ ʣʛʤʥʦʛʚʛʡʛʣʣʤʧʨʞ ʚʡʵ ʪʞʦʢ ʞ ʚʤʢʖʮʣʞʫ ʫʤʝʵʟʧʨʘ
ʓʨʤ ʫʤʦʤʮʤ ʣʖʥʦʞʢʛʦ ʥʤʨʤʢʩ ʭʨʤ ʧʣʞʜʛʣʞʛ ʩʦʤʘʣʵ ʣʛʤʥʦʛʚʛʡʛʣʣʤʧʨʞ ʢʤʜʛʨ ʧʥʤʧʤʗʧʨʘʤ
ʘʖʨʲ ʦʤʧʨʩ ʞʣʘʛʧʨʞʬʞʟ

ʗ ɸʤʝʢʤʜʣʱʛ ʖʦʙʩʢʛʣʨʱ ʘ ʥʤʡʲʝʩ ʩʨʘʛʦʜʚʛʣʞʵ

•

ʇʤʙʡʖʧʣʤ ʠʛʟʣʧʞʖʣʧʠʤʢʩ ʥʤʚʫʤʚʩ ʘʖʜʣʤ ʣʛ ʧʤʧʨʤʵʣʞʛ ʙʤʧʩʚʖʦʧʨʘʛʣʣʤʙʤ ʗʴʚʜʛʨʖ ʖ ʥʦʤ
ʘʛʚʛʣʞʛ ʧʨʖʗʞʡʞʝʖʬʞʤʣʣʤʟ ʪʞʧʠʖʡʲʣʤʟ ʥʤʡʞʨʞʠʞ ʩʘʛʡʞʭʛʣʞʛ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʫ ʦʖʧʫʤʚʤʘ
ʞ ʧʤʠʦʖʯʛʣʞʛ ʣʖʡʤʙʤʘ ʘ ʥʛʦʞʤʚ ʧʥʖʚʖ ʚʡʵ ʧʨʞʢʩʡʞʦʤʘʖʣʞʵ ʚʛʡʤʘʤʟ ʖʠʨʞʘʣʤʧʨʞ ʞʡʞ ʧʤʠʦʖ
ʯʛʣʞʛ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʫ ʦʖʧʫʤʚʤʘ ʞ ʩʘʛʡʞʭʛʣʞʛ ʣʖʡʤʙʤʘʱʫ ʥʤʧʨʩʥʡʛʣʞʟ ʘ ʥʛʦʞʤʚ ʥʛʦʛʙʦʛ
ʘʖ ʳʠʤʣʤʢʞʠʞ ʚʡʵ ʧʣʞʜʛʣʞʵ ʚʛʡʤʘʤʟ ʖʠʨʞʘʣʤʧʨʞ ɸ ʨʖʠʤʟ ʧʞʨʩʖʬʞʞ ʥʤʥʱʨʠʖ ʧʗʖʡʖʣʧʞʦʤ
ʘʖʨʲ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʟ ʗʴʚʜʛʨ ʛʜʛʙʤʚʣʤ ʢʤʜʛʨ ʥʦʞʘʛʧʨʞ ʡʞʗʤ ʠ ʛʯʛ ʗʤʡʲʮʛʢʩ ʥʛʦʛʙʦʛ
ʘʩ ʳʠʤʣʤʢʞʠʞ  ʥʦʞ ʥʤʚʰʛʢʛ ʚʤʫʤʚʱ ʤʨ ʣʖʡʤʙʤʘ ʩʘʛʡʞʭʞʘʖʴʨʧʵ ʝʖ ʧʭʛʨ ʚʛʟʧʨʘʞʵ ʖʘʨʤʢʖʨʞ
ʭʛʧʠʞʫ ʧʨʖʗʞʡʞʝʖʨʤʦʤʘ ʧʡʛʚʤʘʖʨʛʡʲʣʤ ʚʡʵ ʧʨʖʗʞʡʞʝʖʬʞʞ ʗʴʚʜʛʨʖ ʥʦʖʘʞʨʛʡʲʧʨʘʤ ʚʤʡʜʣʤ
ʩʘʛʡʞʭʞʨʲ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʟ ʦʖʧʫʤʚʱ ʭʨʤ ʨʤʡʲʠʤ ʩʧʞʡʞʨ ʥʛʦʛʙʦʛʘ ʳʠʤʣʤʢʞʠʞ ʡʞʗʤ ʠ ʛʯʛ
ʗʤʡʛʛ ʙʡʩʗʤʠʤʢʩ ʧʥʖʚʩ  ʖʣʖʡʤʙʞʭʣʖʵ ʡʤʙʞʠʖ

•

ɺʦʩʙʤʛ ʘʖʜʣʤʛ ʧʤʤʗʦʖʜʛʣʞʛ ʝʖʠʡʴʭʖʛʨʧʵ ʘ ʤʙʦʖʣʞʭʛʣʞʞ

ʤʧʩʯʛʧʨʘʞʢʤʧʨʞ ʛʜʛʙʤʚʣʤʙʤ ʗʖ

ʡʖʣʧʞʦʤʘʖʣʞʵ

 ɺʖʜʛ ʛʧʡʞ ʥʦʛʚʧʨʖʘʞʨʲ ʭʨʤ ʥʦʖʘʞʨʛʡʲʧʨʘʤ ʣʛʧʢʤʨʦʵ ʣʞ ʣʖ ʭʨʤ ʝʖʚʖʡʤʧʲ ʬʛ

ʡʲʴ ʧʗʖʡʖʣʧʞʦʤʘʖʨʲ ʛʜʛʙʤʚʣʱʟ ʗʴʚʜʛʨ ʨʤ ʣʩʜʣʤ ʩʭʞʨʱʘʖʨʲ ʭʨʤ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʛ ʦʖʧʫʤ
ʚʱ ʣʛʘʤʝʢʤʜʣʤ ʧʤʠʦʖʨʞʨʲ ʣʞʜʛ ʠʖʠʤʟʨʤ ʝʣʖʭʞʨʛʡʲʣʤʟ ʥʤʡʤʜʞʨʛʡʲʣʤʟ ʘʛʡʞʭʞʣʱ  ʧʦʛʚʞ
ʥʦʤʭʛʙʤ ʞʝʝʖ ʧʤʬʞʖʡʲʣʱʫ ʦʖʧʫʤʚʤʘ ʖ ʣʖʡʤʙʤʘʱʛ ʥʤʧʨʩʥʡʛʣʞʵ ʤʙʦʖʣʞʭʛʣʱ ʧʘʛʦʫʩ  ʞʝʝʖ
ʥʞʠʖ ʠʦʞʘʤʟ ʁʖʪʪʛʦʖ ɺʤʥʤʡʣʞʨʛʡʲʣʱʢʞ ʧʡʤʜʣʤʧʨʵʢʞ ʢʤʜʛʨ ʧʨʖʨʲ ʤʨʧʩʨʧʨʘʞʛ ʥʤʡʞʨʞʭʛ
ʧʠʤʟ ʦʛʮʞʢʤʧʨʞ ʧʤʠʦʖʨʞʨʲ ʣʛʠʤʨʤʦʱʛ ʧʨʖʨʲʞ ʙʤʧʩʚʖʦʧʨʘʛʣʣʱʫ ʦʖʧʫʤʚʤʘ  ʣʖʥʦʞʢʛʦ ʘʤʛʣ
ʣʱʛ ʦʖʧʫʤʚʱ ʖ ʨʖʠʜʛ ʣʛʘʤʝʢʤʜʣʤʧʨʲ ʧʤʗʦʖʨʲ ʨʦʛʗʩʛʢʱʟ ʤʗʰʛʢ ʣʖʡʤʙʤʘ ʝʖ ʠʤʦʤʨʠʞʟ ʥʦʤ
ʢʛʜʩʨʤʠ ʘʦʛʢʛʣʞ

ɸʤʝʢʤʜʣʱʛ ʖʦʙʩʢʛʣʨʱ ʥʦʤʨʞʘ ʩʨʘʛʦʜʚʛʣʞʵ

•

ʈʦʩʚʣʤʧʨʲ ʥʦʤʙʣʤʝʞʦʤʘʖʣʞʵ

ʍʨʤʗʱ ʗʖʡʖʣʧʞʦʤʘʖʨʲ ʗʴʚʜʛʨ ʘ ʨʛʭʛʣʞʛ ʬʞʠʡʖ ʣʩʜʣʤ ʩʢʛʨʲ

ʥʦʤʙʣʤʝʞʦʤʘʖʨʲ ʗʩʚʩʯʞʛ ʧʨʖʚʞʞ ʬʞʠʡʖ  ʞʫ ʥʦʤʚʤʡʜʞʨʛʡʲʣʤʧʨʲ ʞ ʖʢʥʡʞʨʩʚʩ ɶ ʳʨʤ ʢʤʜʛʨ
ʗʱʨʲ ʝʖʨʦʩʚʣʞʨʛʡʲʣʤ

•

ɶʧʞʢʢʛʨʦʞʭʣʤʧʨʲ ʠʤʡʛʗʖʣʞʟ

ɸ ʦʛʖʡʲʣʤʧʨʞ ʥʤ ʧʘʤʛʟ ʥʦʤʚʤʡʜʞʨʛʡʲʣʤʧʨʞ ʞ ʙʡʩʗʞʣʛ ʧʥʖ

ʚʱ ʭʖʧʨʤ ʝʣʖʭʞʨʛʡʲʣʤ ʗʤʡʲʮʛ ʭʛʢ ʥʤʚʰʛʢʱ ʞ ʥʤʠʦʱʨʲ ʗʴʚʜʛʨʣʱʛ ʚʛʪʞʬʞʨʱ ʝʖ ʧʭʛʨ ʞʝ
ʡʞʮʠʤʘ ʘʦʵʚ ʡʞ ʩʚʖʧʨʧʵ

•

ʅʡʤʫʞʛ ʧʨʞʢʩʡʱ ʚʡʵ ʥʦʖʘʞʨʛʡʲʧʨʘʖ

ʇʢʛʣʱ ʥʦʖʘʞʨʛʡʲʧʨʘ  ʘ ʦʛʝʩʡʲʨʖʨʛ ʘʱʗʤʦʤʘ ʢʤʙʩʨ ʣʛ

ʧʤʘʥʖʚʖʨʲ ʧʤ ʧʢʛʣʤʟ ʗʞʝʣʛʧʬʞʠʡʤʘ ʅʤʳʨʤʢʩ ʩ ʨʛʠʩʯʛʙʤ ʥʦʖʘʞʨʛʡʲʧʨʘʖ ʢʤʙʩʨ ʗʱʨʲ ʧʨʞʢʩ

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

ʡʱ ʚʤʥʩʧʠʖʨʲ ʚʛʪʞʬʞʨʣʱʟ ʗʴʚʜʛʨ ʨʖʠ ʠʖʠ ʦʖʧʥʡʖʭʞʘʖʨʲʧʵ ʧ ʚʤʡʙʖʢʞ ʥʦʞʚʛʨʧʵ ʩʜʛ ʚʦʩʙʤʢʩ
ʥʦʖʘʞʨʛʡʲʧʨʘʩ

ʇʫʛʢʖ ʤʬʛʣʞʘʖʣʞʵ

ɸ ʠʖʜʚʤʢ ʥʩʣʠʨʛ ʨʦʛʗʩʛʨʧʵ ʫʤʨʵ ʗʱ ʤʚʞʣ ʤʗʤʧʣʤʘʖʣʣʱʟ ʖʦʙʩʢʛʣʨ ʘ ʥʤʡʲʝʩ ʞʧʨʞʣʣʤʧʨʞ ʩʨʘʛʦ

ʜʚʛʣʞʵ ʞ ʫʤʨʵ ʗʱ ʤʚʞʣ ʤʗʤʧʣʤʘʖʣʣʱʟ ʖʦʙʩʢʛʣʨ ʥʤʭʛʢʩ ʧ ʩʨʘʛʦʜʚʛʣʞʛʢ ʢʤʜʣʤ ʧʤʙʡʖʧʞʨʲʧʵ
ʡʞʮʲ ʧ ʤʙʤʘʤʦʠʖʢʞ

ɻʧʡʞ ʛʧʨʲ ʖʦʙʩʢʛʣʨ  ʞʡʞ ʖʦʙʩʢʛʣʨʱ ʨʤʡʲʠʤ ʘ ʤʚʣʩ ʧʨʤʦʤʣʩ ʨʤ ʥʩʣʠʨ ʤʬʛʣʞʘʖʛʨʧʵ ʘ  ʗʖʡʡʤʘ

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

ɽʖʚʖʭʖ 

 ʇʥʞʧʱʘʖʨʲ oo ʣʤʦʢʖ 

ʆʖʧʥʦʤʧʨʦʖʣʛʣʞʛ ʠʩʡʲʨʩʦʣʱʫ ʣʤʦʢ oo ʧʡʤʜʣʱʟ ʥʦʤʬʛʧʧ ʠʤʨʤʦʱʟ ʥʤ ʢʣʛʣʞʴ ʣʛʠʤʨʤʦʱʫ ʞʧ

ʧʡʛʚʤʘʖʨʛʡʛʟ ʤʧʣʤʘʖʣ ʣʖ ʠʤʥʞʦʤʘʖʣʞʞ ʥʦʞʝʣʖʠʤʘ ʤʠʦʩʜʖʴʯʞʫ ʅʦʞʭʛʢ ʭʖʧʨʤ ʳʨʤʨ ʥʦʤʬʛʧʧ ʞʚʛʨ
ʣʛʤʧʤʝʣʖʣʣʤ ʞ ʦʖʧʥʦʤʧʨʦʖʣʛʣʣʱʢ ʤʨʘʛʨʤʢ ʣʖʥʦʞʢʛʦ ʣʖ ʘʤʥʦʤʧ

jʅʤʭʛʢʩ ʨʱ ʙʤʘʤʦʞʮʲ ʧ ʨʖʠʞʢ

ʖʠʬʛʣʨʤʢ x

ʗʩʚʛʨ

jʨʩʨ ʘʧʛ ʨʖʠ ʙʤʘʤʦʵʨx

 ʖ ʣʛ

jʵ ʦʖʧʧʢʤʨʦʛʡ ʦʵʚ ʘʤʝʢʤʜʣʱʫ ʖʠʬʛʣʨʤʘ ʞ ʥʤʣʵʡ

ʭʨʤ ʣʖʞʗʤʡʲʮʞʟ ʘʱʞʙʦʱʮ ʢʣʛ ʥʦʞʣʤʧʞʨ ʞʢʛʣʣʤ ʳʨʤʨx

 ʈʖʠʤʟ ʘʱʗʤʦ ʘʥʤʡʣʛ ʢʤʜʛʨ ʤʠʖʝʖʨʲʧʵ

ʦʖʬʞʤʣʖʡʲʣʱʢ ʥʦʞ ʨʤʢ ʭʨʤ ʧʖʢʖ ʣʤʦʢʖ ʢʤʜʛʨ ʗʱʨʲ ʣʛʳʪʪʛʠʨʞʘʣʤʟ ʣʤ ʩʧʨʤʟʭʞʘʤʟ

ɸ ʳʨʤʟ ʝʖʚʖʭʛ ʢʱ ʞʧʧʡʛʚʩʛʢ ʦʖʧʥʦʤʧʨʦʖʣʛʣʞʛ ʣʤʦʢʱ jʧʥʞʧʱʘʖʨʲx ʘ ʮʠʤʡʲʣʤʟ ʧʦʛʚʛ ɷʩʚʛʢ

ʧʭʞʨʖʨʲ ʭʨʤ ʛʧʨʲ ʚʘʖ ʨʞʥʖ ʮʠʤʡʲʣʞʠʤʘ ʨʛ ʠʨʤ ʭʛʧʨʣʤ ʙʤʨʤʘʵʨʧʵ ʠ ʥʦʤʘʛʦʤʭʣʱʢ ʦʖʗʤʨʖʢ ʞ ʣʛ ʧʥʞ
ʧʱʘʖʴʨ ʖ ʨʖʠʜʛ ʨʛ ʠʨʤ ʣʛ ʙʤʨʤʘʵʨʧʵ ʞ ʧʥʞʧʱʘʖʴʨ ʧʤ ʮʥʖʦʙʖʡʤʠ

*

↓

\

**

→

ʍʛʧʨʣʱʟ ʇʥʞʧʱʘʖʛʨ

ʍʛʧʨʣʱʟ

 

−

Ċĉ 

ʇʥʞʧʱʘʖʛʨ

−

Ċĉ

 

ɻʧʡʞ

ʚʘʖ ʭʛʧʨʣʱʫ ʮʠʤʡʲʣʞʠʖ ʧʞʚʵʨ ʦʵʚʤʢ

ʣʖ ʥʦʤʘʛ

ʦʤʭʣʤʟ ʦʖʗʤʨʛ ʨʤ ʤʣʞ ʭʛʧʨʣʤ ʥʞʮʩʨ ʳʨʩ ʦʖʗʤʨʩ ʞ ʚʖʜʛ
ʥʤʡʩʭʖʴʨ ʩʚʤʘʤʡʲʧʨʘʞʛ ʤʨ ʧʘʤʛʟ ʭʛʧʨʣʤʧʨʞ ɷʩʚʛʢ ʧʭʞ
ʨʖʨʲ ʭʨʤ ʠʖʜʚʱʟ ʞʝ ʣʞʫ ʘ ʳʨʤʢ ʧʡʩʭʖʛ ʥʤʡʩʭʖʛʨ ʘʱʞʙʦʱʮ

 ʥʤʡʛʝʣʤʧʨʲ ʦʖʘʣʱʟ  ɻʧʡʞ ʜʛ

ʚʘʖ ʧʥʞʧʱʘʖʴʯʞʫ ʮʠʤʡʲʣʞʠʖ ʧʞʚʵʨ ʦʵʚʤʢ

 ʨʤ ʘʤʥʛʦʘʱʫ ʩ ʣʞʫ

ʥʤʡʩʭʖʛʨʧʵ ʫʩʜʛ ʣʖʥʞʧʖʨʲ ʖ ʘʤʘʨʤʦʱʫ ʤʣʞ ʣʛʦʘʣʞʭʖʴʨ ʢʛʮʖʴʨ ʚʦʩʙ ʚʦʩʙʩ ʞ ʥʦʞʘʡʛʠʖʴʨ ʘʣʞ
ʢʖʣʞʛ ʞʝʝʖ ʭʛʙʤ ʘʱʞʙʦʱʮ ʠʖʜʚʤʙʤ ʦʖʘʛʣ  ɸ ʧʡʩʭʖʛ ʠʤʙʚʖ

ʧʥʞʧʱʘʖʴʯʞʟ ʞ ʭʛʧʨʣʱʟ ʧʞʚʵʨ ʦʵ

ʚʤʢ

 ʧʥʞʧʱʘʖʴʯʞʟ ʥʤʡʩʭʖʛʨ ʘʱʞʙʦʱʮ  ʨʖʠ ʠʖʠ ʧʥʞʧʖʡ ʦʖʗʤʨʩ ʞ ʣʛ ʧʞʡʲʣʤ ʥʦʞʘʡʛʠʖʡ ʠ ʧʛʗʛ

ʘʣʞʢʖʣʞʛ ʖ ʭʛʧʨʣʱʟ ʥʤʡʩʭʖʛʨ ʘʱʞʙʦʱʮ

(

−

Ċĉ

)

 ʨʖʠ ʠʖʠ ʣʛ ʢʤʙ ʣʞʭʛʙʤ ʣʤʦʢʖʡʲʣʤ ʦʛʮʖʨʲ ʞʝʝʖ ʘʤ

ʥʞʴʯʛʟ ʣʛʧʥʦʖʘʛʚʡʞʘʤʧʨʞ ʠʤʨʤʦʖʵ ʨʘʤʦʞʡʖʧʲ ʦʵʚʤʢ ʧ ʣʞʢ

ʉʭʞʨʛʡʲ ʗʤʦʛʨʧʵ ʧʤ ʧʥʞʧʱʘʖʣʞʛʢ ʥʩʨʛʢ ʥʤʧʨʤʵʣʣʤʙʤ ʥʛʦʛʧʖʜʞʘʖʣʞʵ ʮʠʤʡʲʣʞʠʤʘ ɸ ʠʡʖʧʧʛ

 ʩʭʛʣʞʠʖ ʞ ʘ ʨʛʭʛʣʞʛ ʢʛʧʵʬʖ   ʩʭʛʗʣʱʟ ʚʛʣʲ ʠʖʜʚʱʟ ʩʧʥʛʘʖʛʨ ʥʤʧʞʚʛʨʲ ʧ ʠʖʜʚʱʢ ʤʚʣʤ
ʠʡʖʧʧʣʞʠʤʢ ʝʖ ʥʖʦʨʤʟ ʥʤ ʤʚʣʤʢʩ ʦʖʝʩ ʅʤ ʞʨʤʙʖʢ ʢʛʧʵʬʖ ʠʖʜʚʱʟ ʮʠʤʡʲʣʞʠ ʧʦʖʘʣʞʘʖʛʨ ʥʤʡʩʭʛʣ
ʣʱʟ ʧʩʢʢʖʦʣʱʟ ʘʱʞʙʦʱʮ ʧ ʨʛʢ ʘʱʞʙʦʱʮʛʢ ʠʤʨʤʦʱʟ ʤʣ ʥʤʡʩʭʞʡ ʗʱ ʛʧʡʞ ʗʱ ʘʛʧʲ ʢʛʧʵʬ ʘʛʡ ʧʛʗʵ
ʥʤʚʦʩʙʤʢʩ  ʧ ʩʭʛʨʤʢ ʨʤʙʤ ʠʖʠ ʘʛʡʞ ʧʛʗʵ ʤʚʣʤʠʡʖʧʧʣʞʠʞ ɻʧʡʞ ʘ ʥʦʤʮʡʤʢ ʢʛʧʵʬʛ ʩʭʛʣʞʠ ʧʥʞʧʱ
ʘʖʡ ʖ ʗʩʚʩʭʞ ʭʛʧʨʣʱʢ ʥʤʡʩʭʞʡ ʗʱ ʘʱʞʙʦʱʮ ʧʨʦʤʙʤ ʗʤʡʲʮʛ ʘ ʧʡʛʚʩʴʯʛʢ ʢʛʧʵʬʛ ʤʣ ʣʛ ʗʩʚʛʨ
ʧʥʞʧʱʘʖʨʲ ɻʧʡʞ ʤʣ ʘ ʥʦʤʮʡʤʢ ʢʛʧʵʬʛ ʗʱʡ ʭʛʧʨʣʱʢ ʨʤ ʘʱʗʤʦ ʣʛʭʛʧʨʣʤʙʤ ʥʤʘʛʚʛʣʞʵ ʧʘʵʝʖʣ ʧ ʢʤ
ʦʖʡʲʣʱʢʞ ʞʝʚʛʦʜʠʖʢʞ ʨʖʠ ʭʨʤ ʤʣ ʥʛʦʛʠʡʴʭʞʨʧʵ ʨʤʡʲʠʤ ʛʧʡʞ ʤʗʯʞʟ ʘʱʞʙʦʱʮ ʤʨ ʥʛʦʛʠʡʴʭʛʣʞʵ
ʘ ʥʦʤʮʡʤʢ ʢʛʧʵʬʛ ʘʱʦʤʧ ʗʱ ʗʤʡʛʛ ʭʛʢ ʣʖ  ɻʧʡʞ ʳʨʞ ʩʧʡʤʘʞʵ ʣʛ ʘʱʥʤʡʣʵʴʨʧʵ ʨʤ ʩʭʛʣʞʠ ʧʤʫʦʖ
ʣʵʛʨ ʧʘʤʟ ʨʞʥ ʣʖ ʧʡʛʚʩʴʯʞʟ ʢʛʧʵʬ

ʖ   ʗʖʡʡʤʘ

ʅʩʧʨʲ ʘ ʥʛʦʘʤʢ ʢʛʧʵʬʛ ʘ ʠʡʖʧʧʛ ʗʱʡʤ

9

ʭʛʧʨʣʱʫ ʞ

:

ʧʥʞʧʱʘʖʴʯʞʫ ʮʠʤʡʲʣʞʠʤʘ

 

9

ʞ

:

ʢʤʙʩʨ ʥʦʞʣʞʢʖʨʲ ʡʴʗʱʛ ʬʛʡʱʛ ʣʛʤʨʦʞʬʖʨʛʡʲʣʱʛ ʝʣʖʭʛʣʞʵ ʨʖʠʞʛ ʭʨʤ

9

+

:

=

ċċ ʀʖʠ ʗʩʚʛʨ

ʢʛʣʵʨʲʧʵ ʠʤʡʞʭʛʧʨʘʤ ʮʠʤʡʲʣʞʠʤʘ ʠʖʜʚʤʙʤ ʨʞʥʖ ʘ ʧʡʛʚʩʴʯʞʛ ʢʛʧʵʬʱ 

ʗ   ʗʖʡʡʤʘ

ʃʖʝʤʘʛʢ

ʦʖʘʣʤʘʛʧʣʱʢ ʠʡʖʧʧʤʢ

ʨʖʠʤʟ ʘ ʠʤʨʤʦʤʢ ʣʞʠʨʤ ʞʝ ʮʠʤʡʲʣʞʠʤʘ ʥʤ ʞʨʤ

ʙʖʢ ʢʛʧʵʬʖ ʣʛ ʧʨʖʣʛʨ ʢʛʣʵʨʲ ʧʘʤʟ ʨʞʥ ʅʦʛʚʥʤʡʤʜʞʢ ʭʨʤ ʠʡʖʧʧ ʗʱʡ ʦʖʘʣʤʘʛʧʣʱʢ ʠʤʙʚʖ ʤʚʞʣ
ʞʝ ʩʭʛʣʞʠʤʘ  ʣʖʝʤʘʛʢ ʛʙʤ ɸʤʘʤʭʠʖ ʣʖ ʤʚʞʣ ʢʛʧʵʬ ʥʤʢʛʣʵʡ ʧʘʤʟ ʨʞʥ ʣʞ ʧ ʨʤʙʤ ʣʞ ʧ ʧʛʙʤ  ʥʤʧʡʛ
ʳʨʤʙʤ ʢʛʧʵʬʖ ʤʣ ʧʣʤʘʖ ʧʨʖʣʛʨ ʤʗʱʭʣʱʢ ʩʭʛʣʞʠʤʢ ʦʖʬʞʤʣʖʡʲʣʤ ʧʦʖʘʣʞʘʖʴʯʞʢ ʘʱʙʤʚʱ ʀʖʠ ʗʩ
ʚʛʨ ʢʛʣʵʨʲʧʵ ʠʤʡʞʭʛʧʨʘʤ ʮʠʤʡʲʣʞʠʤʘ ʠʖʜʚʤʙʤ ʨʞʥʖ ʘ ʧʡʛʚʩʴʯʞʛ ʢʛʧʵʬʱ 

 ʖʥʦʛʡʵ  ʙ

ʟ ʨʩʦ ɽʖʚʖʭʞ

ʘ   ʗʖʡʡʤʘ

ɻʧʡʞ ʘʱ ʥʦʖʘʞʡʲʣʤ ʦʛʮʞʡʞ ʥʩʣʠʨʱ

ʖ

ʞ

ʗ

 ʨʤ ʩ ʘʖʧ ʚʤʡʜʣʤ ʗʱʡʤ ʥʤʡʩʭʞʨʲ

ʧʵ ʭʨʤ ʧʩʯʛʧʨʘʩʛʨ ʣʛʧʠʤʡʲʠʤ ʨʞʥʤʘ ʦʖʘʣʤʘʛʧʣʱʫ ʠʡʖʧʧʤʘ ʥʦʞʭʛʢ ʤʚʞʣ ʞʝ ʣʞʫ ʵʘʡʵʛʨʧʵ ʧʖʢʱʢ
ʥʦʛʚʥʤʭʨʞʨʛʡʲʣʱʢ ʚʡʵ ʠʖʜʚʤʙʤ ʮʠʤʡʲʣʞʠʖ ʅʦʛʚʥʤʡʤʜʞʢ ʩʭʞʨʛʡʲ ʞʝʣʖʭʖʡʲʣʤ ʝʣʖʛʨ ʠ ʠʖʠʤ
ʢʩ ʨʞʥʩ ʥʦʞʣʖʚʡʛʜʞʨ ʠʖʜʚʱʟ ʮʠʤʡʲʣʞʠ ʞ ʢʤʜʛʨ ʧʤʧʨʖʘʡʵʨʲ ʡʴʗʤʟ ʥʡʖʣ ʦʖʧʧʖʚʠʞ ʣʖ ʠʖʜʚʱʟ
ʚʛʣʲ  ʣʛʤʗʵʝʖʨʛʡʲʣʤ ʚʛʡʖʨʲ ʨʖʠ ʭʨʤʗʱ ʠʖʜʚʱʟ ʧʞʚʛʡ ʧ ʠʖʜʚʱʢ ʘ ʨʛʭʛʣʞʛ ʢʛʧʵʬʖ ʅʦʞ ʠʖʠʤʢ ʢʞ
ʣʞʢʖʡʲʣʤʢ ʝʣʖʭʛʣʞʞ

9

ʩʭʞʨʛʡʴ ʩʚʖʧʨʧʵ ʚʤʗʞʨʲʧʵ ʭʨʤʗʱ ʭʛʦʛʝ ʠʤʣʛʭʣʤʛ ʭʞʧʡʤ ʢʛʧʵʬʛʘ ʠʡʖʧʧ

ʤʠʖʝʖʡʧʵ ʘ ʥʦʛʚʥʤʭʨʞʨʛʡʲʣʤʢ ʦʖʘʣʤʘʛʧʞʞ  ʇʭʞʨʖʟʨʛ ʭʨʤ jʘʤʘʤʭʛʠx ʘ ʠʡʖʧʧʛ ʣʛʨ ʨʤ ʛʧʨʲ ʘʧʛ ʥʦʞ
ʣʞʢʖʴʨ ʦʛʮʛʣʞʵ ʨʖʠ ʠʖʠ ʤʥʞʧʖʣʤ ʘ ʝʖʚʖʭʛ

ʆʛʮʛʣʞʛ

ʖ

 ʅʦʛʚʥʤʡʤʜʞʢ ʘ ʠʡʖʧʧʛ ʛʧʨʲ ʭʛʧʨʣʱʛ ʮʠʤʡʲʣʞʠʞ ʨʤ ʛʧʨʲ

9

>

ĉ ɸ ʥʛʦʘʤʢ ʢʛʧʵʬʛ ʠʖʜʚʱʟ

ʨʖʠʤʟ ʮʠʤʡʲʣʞʠ

(

9

−

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)

ʦʖʝ ʘʧʨʦʛʨʞʡʧʵ ʧ ʧʛʗʛ ʥʤʚʤʗʣʱʢʞ  ʞ ʠʖʜʚʱʟ ʦʖʝ ʥʤʡʩʭʞʡ  ʞ

:

ʦʖʝ oo ʧʤ

ʧʥʞʧʱʘʖʡʲʯʞʠʖʢʞ  ʞ ʠʖʜʚʱʟ ʦʖʝ ʥʤʡʩʭʞʡ

−

Ċĉ ʈʖʠʞʢ ʤʗʦʖʝʤʢ ʛʙʤ ʘʱʞʙʦʱʮ ʗʱʡ ʦʖʘʛʣ

6

ʭ

=

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(

9

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Ċ

)

−

Ċĉ

:

.

ɻʧʡʞ ʤʣ ʘ ʥʛʦʘʤʢ ʢʛʧʵʬʛ ʧʡʛʚʤʘʖʡ ʗʱ ʚʦʩʙʤʟ ʣʤʦʢʛ ʨʤ ʭʛʧʨʣʱʫ ʮʠʤʡʲʣʞʠʤʘ ʧʨʖʡʤ ʗʱ

(

9

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Ċ

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 ʖ

ʧʥʞʧʱʘʖʴʯʞʫ oo

(

:

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)

 ʞ ʘʱʞʙʦʱʮ ʥʛʦʛʠʡʴʭʞʘʮʛʙʤʧʵ ʮʠʤʡʲʣʞʠʖ ʗʱʡ ʗʱ ʦʖʘʛʣ

(

Ď

(

9

−

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−

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 ʧ ʩʭʛʨʤʢ ʢʤʦʖʡʲʣʱʫ ʞʝʚʛʦʜʛʠ ʍʛʧʨʣʱʟ ʮʠʤʡʲʣʞʠ ʤʧʨʖʣʛʨʧʵ ʭʛʧʨʣʱʢ ʛʧʡʞ

Ċĉ

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)

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ʨʤ ʛʧʨʲ  ʧ ʩʭʛʨʤʢ ʨʤʙʤ ʭʨʤ

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9

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Ċč ɻʧʡʞ ʜʛ

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Ċč ʨʤ ʛʧʨʲ ʭʛʧʨʣʱʫ ʮʠʤʡʲʣʞʠʤʘ ʚʤʧʨʖʨʤʭʣʤ

ʢʖʡʤ ʨʤ ʘʧʛ ʤʣʞ ʥʛʦʛʠʡʴʭʖʨʧʵ ʣʖ ʣʛʭʛʧʨʣʤʛ ʥʤʘʛʚʛʣʞʛ ʘ ʧʡʛʚʩʴʯʛʢ ʢʛʧʵʬʛ

 ʅʦʛʚʥʤʡʤʜʞʢ ʘ ʠʡʖʧʧʛ ʛʧʨʲ ʧʥʞʧʱʘʖʴʯʞʛ ʮʠʤʡʲʣʞʠʞ ʨʤ ʛʧʨʲ

:

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ĉ ɸ ʥʛʦʘʤʢ ʢʛʧʵʬʛ

ʠʖʜʚʱʟ ʨʖʠʤʟ ʮʠʤʡʲʣʞʠ

(

:

−

Ċ

)

ʦʖʝ ʘʧʨʦʛʨʞʡʧʵ ʧ ʧʛʗʛ ʥʤʚʤʗʣʱʢʞ  ʞ ʠʖʜʚʱʟ ʦʖʝ ʥʤʡʩʭʞʡ  ʞ

9

ʦʖʝ oo ʧ ʭʛʧʨʣʱʢʞ  ʞ ʠʖʜʚʱʟ ʦʖʝ ʥʤʡʩʭʞʡ  ʈʖʠʞʢ ʤʗʦʖʝʤʢ ʛʙʤ ʘʱʞʙʦʱʮ ʗʱʡ ʦʖʘʛʣ

6

ʧ

=

Ď

9

.

ɻʧʡʞ ʤʣ ʘ ʥʛʦʘʤʢ ʢʛʧʵʬʛ ʧʡʛʚʤʘʖʡ ʗʱ ʚʦʩʙʤʟ ʣʤʦʢʛ ʨʤ ʭʛʧʨʣʱʫ ʮʠʤʡʲʣʞʠʤʘ ʧʨʖʡʤ ʗʱ

(

9

+

Ċ

)

 ʖ

ʧʥʞʧʱʘʖʴʯʞʫ oo

(

:

−

Ċ

)

 ʞ ʘʱʞʙʦʱʮ ʥʛʦʛʠʡʴʭʞʘʮʛʙʤʧʵ ʮʠʤʡʲʣʞʠʖ ʗʱʡ ʗʱ ʦʖʘʛʣ

(

Ċĉ

9

−

Ċĉ

(

:

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Ċ

))

ʇʥʞʧʱʘʖʴʯʞʟ ʮʠʤʡʲʣʞʠ ʤʧʨʖʣʛʨʧʵ ʧʥʞʧʱʘʖʴʯʞʢ ʛʧʡʞ

Ď

9

⩾

Ċĉ

9

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(

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,

ʨʤ ʛʧʨʲ  ʧ ʩʭʛʨʤʢ ʨʤʙʤ ʭʨʤ

:

=

ċċ

−

9

9

⩽

Ċč ɻʧʡʞ ʜʛ

9

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Ċč ʨʤ ʛʧʨʲ ʭʛʧʨʣʱʫ ʮʠʤʡʲʣʞʠʤʘ ʚʤʧʨʖʨʤʭʣʤ

ʢʣʤʙʤ ʨʤ ʘ ʧʡʛʚʩʴʯʛʢ ʢʛʧʵʬʛ ʘʧʛ ʣʛʭʛʧʨʣʱʛ ʧʨʖʣʩʨ ʭʛʧʨʣʱʢʞ