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µ±xÇ÷½üÓÚ0ʱ,xsinÇ÷ÓÚ¶àÉÙ
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µ±X½Ó½üÓÚÎÞÏÞʱ,Çóxsin(1/x)µÄ¼«ÏÞ
xsin(1/x)=(sin(1/x))/(1/x)µ±xÇ÷ÏòÓÚÎÞÇî´ó,1/xÈ¥ÏòÎÞÇîС,¹Ê(sint)/t µ±tÇ÷ÏòÓÚÎÞÇîСʱ,´ËʽÇ÷ÏòÓÚ1¹Ê´ð°¸Îª1
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xsin(1/x)=sin(1/x)/(1/x),ËùÒÔµ±xÇ÷ÏòÓëÎÞÇîʱµÈÓÚ1£¬µ±Ç÷ÏòÓÚ0ʱ¼«ÏÞΪ0£¬ÒòΪ´Ëʱº¯Êýsin(1/x)Óн磬Íû²ÉÄÉ¡£¡£Áîy=1/xÔòÔʽ=sin(y)/y,µ±yÇ÷ÏòÓÚ...
xsin(kx)¶Ôx»ý·ÖÊÇʲô
»Ø´ð£º·Ö²¿»ý·Ö:Ôʽ=-1/k*¡Òxd(coskx) =-1/kxcoskx+1/k¡Òcoskxdx =-1/kxcoskx+1/k^2sinkx+C
xÇ÷Ïò1,xsin(1/x)ÓÐûÓм«ÏÞ,ÓеϰÊǶàÉÙ?
ÓеϰÊǶàÉÙ£¿º¯Êýxsin(1x)ÔÚµãx=1´¦ÊÇÁ¬ÐøµÄ£¬¸ù¾ÝÁ¬ÐøµÄ¶¨Ò壬limx¡ú1xsin(1x)=xsin(1x)|x=1=sin1.º¯ÊýµÄͼÐÎÊÇÕâÑùµÄ ...
Çó¶þ½×Æ«µ¼Êýz=xsin(x+y)
z=xsin(x+y)∂z/∂x=sin(x+y)+xcos(x+y)∂z/∂y=xcos(x+y)∂²z/∂x²=cos(x+y)+cos(x+y)-xsin(...
xsin(1/x)ÔÚÇóµ¼Ê±ÔõôÇó?ͻȻÁ¬ÓöËĸöÕâÖÖÌâ.ºÜ²»¿ª...
f¡®(x)=[1*sin(1/x)+x*cos(1/x)]*(-1/x^2)=(-1/x^2)*sin(1/x)-(1/x)*cos(1/x)
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