21f08-23 - Å ÅÓÖ ÌÀ ¾½¸ Ü ÑÔР׺ x2 +2x−1...

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Unformatted text preview: Å ÅÓÖ ÌÀ ¾½¸ Ü ÑÔР׺ x2 +2x−1 º x3 −3x2 +2 Ü ÑÔÐ ½º ÓÑÔÙØ limx→3 Ü ÑÔÐ ¾º ÓÑÔÙØ limx→−1 ÈÖÓÓ º ÌÓ Ö¸ Û Ö ÐÐÝ √ x3 + 2x + 7º ÓÒ³Ø Ú Ø Ø x→−1 = lim x→−1 Ü ÑÔÐ ¿º ÓÑÔÙØ ¾º¾º Ä Ñ Ø Ì ×ÓÑ Ì ÖØ limx→9 ÓÖ Ñ׺ Ì × ×¸ ÙØ Û x3 + 2x + 7 lim Ò ÖÙ × ÑÔÐÝ Ø Ø¸ × Ò x3 + 2x + 7, x→−1 limx→−1 x3 + 2x + 7 = (−1)3 + 2(−1) + 7 = 4¸ Ò ÑØ x3 + 2x + 7 lim x→−1 Ø ÓÖÝ ØÓ Ð 2 lim x3 + 2x + 7 = Ó Äĸ ¾¼¼ Ø Ò limx→−1 √ x3 + 2x + 7 = 2º x2 −81 √ º x −3 ØÛÓ Ö ×ÙÐØ× Ñ Ý × ÑÖ Ø Ö Ó Ú ÓÙ׸ ÙØ Ø Ý Û ÐÐ ÐÔ Ñ × Ò× Ö Ò ×ØÝ Ð Ñ Ø׺ ÓÖ Ñ ½º Á Ò f (x) ≤ g(x) ÓÖ ÐÐ x Ò Ò ÓÔ Ò ÒØ ÖÚ Ð Ø Ø ÓÒØ Ò× a ´ Ü ÔØ ÔÓ×× ÐÝ Ø a Ø× Ð ¸ lim f (x) ≤ lim g(x). x→ a Ì ÓÖ Ñ ¾º Ì ´ Ü ÔØ ÔÓ×× ÐÝ ËÕÙ Ø Þ Ì ÓÖ Ñ℄ x→ a Á f (x) ≤ g(x) ≤ h(x) Ò Ò ÓÔ Ò ÒØ ÖÚ Ð Ø a Ø× Ð ¸ Ò lim f (x) = L = lim h(x), Ø x→ a Ò x→ a lim g(x) = L. x→ a Ü ÑÔÐ º Ë ÓÛ Ø Ø lim x sin x→ 0 ¹Ñ Ð Ö ×× Ú º Ó Ò×ÓÒÐ º Ù ½ 1 x =0 Ø ÓÒØ Ò× a ...
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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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