21f08-310 - AFA9 h eD ieÖeÒ Ø ia ÐaÒd iÒ ea ÖA ÔÔ...

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Unformatted text preview: AFA9 h eD ieÖeÒ Ø ia ÐaÒd iÒ ea ÖA ÔÔ ÖÓÜ iÑ a Ø iÓÒ h ee ibÒ iÞÒÓ Øa Ø iÓÒ fÓ Öd e Ö iÚa Ø iÚ e× df/dx i×Ò Ø×ÙÔÔÓ ×ed ØÓÑ eaÒa fÖaØ iÓÒ Öea ÐÐÝB Ù ØiÒ Öea ÐiØÝ iØdÓe×haÚ e×ÓÑ eÑ eaÒ iÒg Ðik eØha ØiÒe Øh ed e Ö iÚa Ø iÚ e i×Øh e ÐiÑ iØ Ó ffÖaØ iÓÒ × if h i× Ò ea Ö a Øh eÒ ( f ( a + h )- f ( a )) /h Û iÐÐb e Ò ea Ö f ′ ( a ) ha Øi×ÖeÔ Ða iÒg a + h bÝ Øh eÑ Ó ÖegeÒ e Ö i x aÒd h bÝ x- a : f ( x )- f ( a ) x- a ≈ f ′ ( a ) , Ó Ö×Ó ÐÚ iÒg fÓ Ö f ( x ) f ( x ) ≈ f ( a ) + f ′ ( a )( x- a ) . A ÒÓ Øh e ÖÛ aÝ ØÓ ÐÓÓka ØØh i× i×Øha ØØh eeÕÙa Ø iÓÒÓ fØh eØaÒgeÒ Ø ÐiÒ e L ØÓ Øh eÙ ÖÚ e y = f ( x ) a Ø ( a, f ( a )) i× y = f ( a ) + f ′ ( a )( x- a ) iÒeØh eØaÒgeÒ Ø ÐiÒ e i×Ò ea ÖØh eg ÖaÔh Øh e y Û iÐÐb e a ÐÑ Ó × Ø Øh e×aÑ ea × f ( x ) h eÔÓ iÒ Øh e Öe i×ØÓaÔÔ ÖÓÜ iÑ a Øe f ( x ) Û h ihÑ igh Øb eaÚ e ÖÝÓÑ Ô Ðia Øed fÙÒ Ø iÓÒbÝa× iÑ Ô Ðe Ö...
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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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21f08-310 - AFA9 h eD ieÖeÒ Ø ia ÐaÒd iÒ ea ÖA ÔÔ...

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