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#1
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ÅÔÁÔµ¢Í§¿Ñ§¡ìªÑ¹
¨§ËÒ¤èÒÅÔÁÔµ¢Í§ $\lim_{x \to 0}\frac{\frac{1}{\sqrt{9+x} }-\frac{1}{3} }{x}$
02 ¡Ã¡®Ò¤Á 2013 18:48 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ truetaems |
#2
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ÍéÒ§ÍÔ§:
àʹÍÇÔ¸Õ¾×é¹°Ò¹ãËé¤ÃѺ Åͧãªé conjugate ¤Ù³·Ñé§àÈÉáÅÐÊèǹ´Ù¤ÃѺ ·ÓãËéÍÂÙèã¹ÃÙ»àÈÉÊèǹ $\frac{3-\sqrt{9+x}}{3(x)\sqrt{9+x} }$ áÅéÇ¡çàÍҤ͹¨Ùࡵ ($3+\sqrt{9+x}$) ¤Ù³·Ñé§àÈÉáÅÐÊèǹ |
#3
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ÇԸբͧ·èÒ¹ËÂÔ¹ËÂÒ§
$\frac{3-\sqrt{9+x}}{3x\sqrt{9+x}}$ $\frac{(3-\sqrt{9+x})(3+\sqrt{9+x})}{3x\sqrt{9+x}(3+\sqrt{9+x})}$ $=\frac{-x}{9x\sqrt{9+x}+3x(9+x)}$ $=\frac{-1}{9\sqrt{9+x}+3(9+x)}$ $\therefore \lim_{x \to 0}\frac{\frac{1}{\sqrt{9+x}}-\frac{1}{3}}{x} =\frac{-1}{27+27}=-\frac{1}{54}$ |
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