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a4_soln

# a4_soln - a Øh7 A ×× igÒÑ eÒ Ø4Ó ÐÙ Ø iÓÒ × D...

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Unformatted text preview: a Øh7 A ×× igÒÑ eÒ Ø4Ó ÐÙ Ø iÓÒ × D eØeÖÑ iÒ ea ÐÐÔÓ iÒ Ø×Û h eÖeØh e fÙÒ cØ iÓÒ i×d ieÖeÒ Ø iab Ðe a f ( x, y ) = braceleftBigg x 4- y 4 x 2 + y 2 , if ( x, y ) negationslash = (0 , 0) , if ( x, y ) = (0 , 0) . Ó ÐÙ Ø iÓÒ :ehaÚ e f x = 4 x 3 ( x 2 + y 2 )- 2 x ( x 4- y 4 ) ( x 2 + y 2 ) 2 , f y =- 4 y 3 ( x 2 + y 2 )- 2 y ( x 4- y 4 ) ( x 2 + y 2 ) 2 . B Ý Øh ecÓÒ Ø iÒÙ iØÝ Øh eÓ ÖeÑ ×bÓ Øha ÖecÓÒ Ø iÒÙÓÙ ×fÓ Öa ÐÐ ( x, y ) negationslash = (0 , 0) h eÒ ce f i×d ieÖeÒ Ø iab Ðe fÓ Öa ÐÐ ( x, y ) negationslash = (0 , 0) Òa ×× igÒÑ eÒ Ø# a Û eÔ ÖÓÚ ed Øha Ø f i×d ieÖeÒ Ø iab Ðea Ø (0 , 0) eÒ ce f i×d ieÖeÒ Ø iab Ðe fÓ Öa ÐÐ ( x, y ) ∈ R 2 b g ( x, y ) = | xy | Ó ÐÙ Ø iÓÒ :ehaÚ e g x = x | y | | x | , g y = y | x | | y | . B Ý Øh ecÓÒ Ø iÒÙ iØÝ Øh eÓ ÖeÑ g x aÒd g y a ÖebÓ Øh cÓÒ Ø iÒÙÓÙ ×fÓ Öa ÐÐ ( x, y ) ∈ R 2 ×Ù ch Øha Ø x negationslash = 0 Ó Ö y negationslash = 0 C ÓÒ × id eÖÔÓ iÒ Ø× (0 , b ) h eÒ g x (0 , b ) = lim h → g (0 + h, b )- g (0 , b ) h = lim h → | bh | h ....
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a4_soln - a Øh7 A ×× igÒÑ eÒ Ø4Ó ÐÙ Ø iÓÒ × D...

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