21f08-33 - AFA8 D eÖ iÚa Ø iÚ e ×Ó fØÖ igÓÒÓÑ e...

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Unformatted text preview: AFA8 D eÖ iÚa Ø iÚ e ×Ó fØÖ igÓÒÓÑ e ØÖ ifÙÒ Ø iÓÒ × ÒÓ Öd e ÖØÓÒd Øh ed e Ö iÚa Ø iÚ eÓ f sin x Û eÖ×Ø Ò eed ØÓÒd ×ÓÑ e ÐiÑ iØ× iÒÚÓ ÐÚ iÒg ØÖ igÓÒÓÑ e ØÖ ifÙÒ Ø iÓÒ ×F iÖ×ØÛ ed ea ÐÛ iØh Øh e ÐiÑ iØ lim x → sin( x ) x . ÓaÔÔ ÐÝ Øh e×ÕÙ eeÞeÔ Ö iÒ iÔ ÐeØÓ Øh i×× iØÙa Ø iÓÒÛ eÒ eed ØÓ ÐÓÓk fÓ ÖfÙÒ Ø iÓÒ ×ÓÒe iØh e Ö× id eØÓ ÓÑ Ôa Öe iØØÓh eÔ iØÙ Öeb e ÐÓÛ ×hÓÛ ×Û ha ØÛ eÒ eedh ea ÖeaÓ fØh e×eØÓ Ö OAB Ó fØh eÙÒ iØ iÖ Ðe i× θ/ 2 a ÖeaÓ fa iÖÙ Ða Ö×eØÓ ÖÛ iØh iÒ ÐÙd edaÒg Ðe θ i× θr 2 / 2 Û h e Öe r i×Øh eÖad iÙ ××Ó ifØh e iÖ Ðe i×aÙÒ iØiÖ Ðe r = 1 Û ehaÚ eÛ ha ØÐa iÑ ed ÓÛ Øh ea ÖeaÓ fØh eØÖ iaÒg Ðe OAB i× 1 2 sin θ × iÒe sin θ i× iØ×h e igh ØaÒd Øh eba ×e i×h ea ÖeaÓ f Øh eÓ Øh e ÖØÖ iaÒg Ðe OBD i× 1 2 tan θ × iÒe iØ i×a Ö igh ØØÖ iaÒg ÐeÛ iØhba ×eaÒdh e igh Ø tan θ Û h ih ÝÓÙaÒ ×eebÝ ØÙ ÖÒ iÒg Øh eÔ iØÙ ÖeÙÔ × id edÓÛ Ò θ 1 B O A sin( ) tan( ) D θ θ 1 Óh a Ø? hÓ ×eØh ÖeeÖeg iÓÒ ×a Öea ÖÖaÒged...
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This note was uploaded on 11/24/2011 for the course MATH 21 taught by Professor Stanley during the Fall '09 term at Lehigh University .

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21f08-33 - AFA8 D eÖ iÚa Ø iÚ e ×Ó fØÖ igÓÒÓÑ e...

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