Lecture10 - ÒÒ iØee Ö ie × F ÖÓÑ Øh eeÜaÑ Ô...

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Unformatted text preview: ÒÒ iØee Ö ie × F ÖÓÑ Øh eeÜaÑ Ô Ðe×Û eÚ ed i×cÙ ××ed ×Ó fa ÖiØaÔÔ ea Ö×Øha ØØh eaccÙ ÖacÝÓ fÓÙ Ö aÝ ÐÓ ÖÓ ÐÝÒÓÑ ia ÐaÔÔ ÖÓÜ iÑ a Ø iÓÒ × Ù ×Ùa ÐÐÝ iÑ Ô ÖÓÚ e×Û h eÒÛ eaddÑ Ó ÖeØeÖÑ × Ò fac ØfÓ Ö×ÓÑ e fÙÒ c Ø iÓÒ ×Øh i×hÓ Ðd ×ØÖÙ eeÚ eÒÛ h eÒÛ ecÓÒ × id eÖÚa ÐÙ e×Ó f x Û h icha ÖeÒ ØÖea ÐÐÝa ÐÐØha Øc ÐÓ ×eØÓ Øh eceÒ ØeÖÓ fØh eÔÓ ÐÝÒÓÑ ia Ð×A ×aÒ eÜaÑ Ô ÐecÓÒ × id eÖ f ( x ) = sin x : f ( x ) = sin x f (0) = 0 f prime ( x ) = cos x f prime (0) = 1 f primeprime ( x ) =- sin x f primeprime (0) = 0 f primeprimeprime ( x ) =- cos x f primeprimeprime (0) =- 1 f (4) ( x ) = sin x f (4) (0) = 0 f (2 n +1) (0) = (- 1) n , f (2 n ) (0) = 0 , = ⇒ P 2 n +1 , ( x ) = x- x 3 3! + x 5 5!- x 7 7! + ··· + (- 1) n x 2 n +1 (2 n + 1)! = n summationdisplay k =0 (- 1) k x 2 k +1 (2 k + 1)! E Ú eÒ ifÛ ecÓÒ × id eÖaÖe Ða Ø iÚ e ÐÝ Ða ÖgeÚa ÐÙ e×aÝ x = 3 , Û eÒd Øha ØÛ iØh eÒÓÙgh ØeÖÑ ×Û eÓb Øa iÒa Öea ×ÓÒab ÐeaÔÔ ÖÓÜ iÑ a Ø iÓÒÓ fØh e fÙÒ c Ø iÓÒÚa ÐÙ e : P 1 , (3) = 3 P 3 , (3) =- 1 . 5 P 5 , (3) = 0 . 525 P 7 , (3) = 0 . 091 P 9 , (3) = 0 . 145 P 11 , (3) = 0 . 141 P 13 , (3) = 0 . 141 Øh e×eÕÙ eÒ cedÓe× iÒd eedcÓÒÚ eÖgeØÓ sin (3)) . Ò fac ØiØØÙ ÖÒ ×ÓÙ ØØha ØØh i× Û iÐÐhaÔÔ eÒ fÓ Ö aÒ Ý chÓ iceÓ f x ; F igÙ Öe ×hÓÛ ×hÓÛ Øh eaÝ ÐÓ ÖÓ ÐÝÒÓÑ ia Ð aÔÔ ÖÓÜ iÑ a Ø iÓÒ ×Ñ a Øch Øh ecÙ ÖÚ e y = sin x ÓÚ eÖ ÐÓÒgeÖaÒd ÐÓÒgeÖ iÒ ØeÖÚa Ð×a × n iÒ cÖea ×e× ÓÛ eÚ eÖØh iÒg ×dÓÒ Ø a ÐÛ aÝ × haÔÔ eÒ Øh i×Û aÝ !C ÓÒ × id eÖØh e fÙÒ c Ø iÓÒ f ( x ) = 1 1+ x . h i×Ø iÑ eÛ eÒd f ( x ) = 1 1+ x f (0) = 1 f prime ( x ) =- 1 (1+ x ) 2 f prime (0) =- 1 f primeprime ( x ) = 2 (1+ x ) 3 f primeprime (0) = 2 f primeprimeprime ( x ) =- 3 (1+ x ) 4 f primeprimeprime (0) =- 3 f ( n ) ( x ) = (- 1) n n !...
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Lecture10 - ÒÒ iØee Ö ie × F ÖÓÑ Øh eeÜaÑ Ô...

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