a4 - ÅØ ¾¿ ×× ÒÑ ÒØ Ù Ö Ý¸ ÂÙÒ Ø ½º Ø...

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Unformatted text preview: ÅØ ¾¿ ×× ÒÑ ÒØ Ù Ö Ý¸ ÂÙÒ Ø ½º Ø ÖÑ Ò ÐÐ ÔÓ ÒØ× Û Ö Ø x 4 −y 4 , x 2 +y 2 ÙÒ Ø ÓÒ × Ö ÒØ Ðº µ f (x, y ) = 0, (x, y ) = (0, 0) (x, y ) = (0, 0). µ g (x, y ) = |xy |º µ h(x, y ) = x √ 4/3 y 1/3 x 2 +y 2 , (x, y ) = (0, 0) (x, y ) = (0, 0). 0, ¾º Ä Ø F = F (x, y, t)¸ x = x(s, t) Ò y = y (s, t) Ò Ò w(s, t) = F (x(s, t), y (s, t), t)º ÏÖ Ø Ø Ò ÖÙÐ ÓÖ ws Ò wt º ËØ Ø ÒÝ ××ÙÑÔØ ÓÒ× ÝÓÙ Ò ØÓ Ñ º Ä Ø f (s, t) = xexy Û Ø x = x(s, t) = (s + 2t)2 Ò y = y (s, t) = cos(st)º Ò fs Ò ft º 2 ¿º º ÓÖÓØ Ý³× ÔÓ× Ø ÓÒ Ø ÒÝ Ø Ñ t ≥ 0 × Ú Ò Ý (x, y, z ) = (t cos t, 2t sin t, t2 )º Ì Ö Ø ÑÔ Ö ØÙÖ Ø ÒÝ ÔÓ ÒØ (x, y, z ) × Ú Ò Ý ÙÒ Ø ÓÒ T : R3 → Rº Á T (−π, 0, π 2 ) = (1, −1, 2) Ø Ò Ø ÖÑ Ò Ø Ö Ø Ó Ò Ó Ø ÑÔ Ö ØÙÖ ÓÖÓØ Ý ÜÔ Ö Ò × Ø Ø Ñ t = π º ...
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This note was uploaded on 11/18/2010 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.

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