sinax - sinbx »¯³É³Ë»ýÐÎʽ(a²»µÈÓÚb)

ÀûÓúͲ»ý¹«Ê½sin ¦Á-sin ¦Â=2cos[(¦Á+¦Â)/2]¡¤sin[(¦Á-¦Â)/2]¿ÉµÃsinax-sinbx=2cos{[(a+b)x]/2}*sin{[(a-b)x]/2}²»Ã÷°×¿ÉÒÔ×·ÎÊ£¬Èç¹ûÓаïÖú...


...e^bx)/(sinax - sinbx) [a¡Ùb]ÀÏʦ˵ֻÄÜÔڳ˻ý״̬...

e^ax=1+ax+o(x),¿ÉµÃµ½:e^ax-e^bx=(a-b)x+o(x)sinax=ax+o(x^2),¿ÉµÃµ½:sinax-sinbx=ax-bx+o(x^2)¼«ÏÞ=1


΢»ý·Ö¼«ÏÞÌâÄ¿ lim(x - >0)(sinax - sinbx)/x

lim(x->0)(sinax-sinbx)/x =lim(x->0) sinax/x-lim(x->0) sinbx/x =a-b


µ±x - >0Çó¼«ÏÞe^ax - e^bx/sinax - sinbxx - >0¾ÍÊÇxÇ÷ÓÚ0...

µ±x->0Çó¼«ÏÞe^ax-e^bx/sinax-sinbx x->0¾ÍÊÇxÇ÷ÓÚ0 ɨÂëÏÂÔØ×÷Òµ°ï ËÑË÷´ðÒÉÒ»ËѼ´µÃ ´ð°¸½âÎö ²é¿´¸ü¶àÓÅÖʽâÎö ½â´ðÒ» ¾Ù±¨ ÏÂÃæÊ¹ÓõÄÊǵȼÛÎÞÇîС(ÂޱȴïÒ»²½¾Í³öÀ´ÁË)...


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b¡ÊZ),ÔÚÒ»ÖÜÆÚ[0,2¦Ð)ÉÏ£º¡¤ ²¨·åÊýΪb¡¤ SinaxÓësinbx½»µãÊýΪ2b¡¤ SinaxÓëf(x)½»µãÊýΪ2b¡¤ SinbxÓëf(x)½»µãÊýΪ2a¡¤ Sinax+...


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·Öĸ¿ÉÒÔÓúͲ»ý¹«Ê½ sinaxÒ»sinbx=2cos((a+b)x/2)sin((aÒ»b)x/2)ËùÒÔ·ÖĸµÈ¼ÛÓÚ (aÒ»b)x/2 ËùÒÔÔ­¼«ÏÞµÈÓÚÒ»2 Íû²ÉÄÉ x...


question lim(x¡ú¡Þ)(e^ax - e^bx)/(sinax - sinbx...

x)e£Þbx=1+bx+o(x)sinax=1-ax+o(x^2)sinbx=1-bx+o(x^2)ËùÒÔ£ºlim(x¡ú0£©(e£Þax-e£Þbx)/(sinax-sinbx) =lim(a-b)x/(-a+b)x=-1 ...


f(x)=x/[a+e^(bx)] ÔÚ( - ¡Þ,+¡Þ)ÄÚÁ¬Ðø,xÔÚ - ¡ÞÊǼ«ÏÞΪ...

,ËùÒÔa>=0½âÎö¿´²»¶®?Ãâ·Ñ²é¿´Í¬ÀàÌâÊÓÆµ½âÎö²é¿´½â´ðÏàËÆÎÊÌâ f(x)={e^x+1 x>0 2x+bx¡Ü0 bΪºÍֵʱ,f(x)¼«ÏÞ´æÔÚ.µ±x->0Çó¼«ÏÞe^ax-e^bx/sinax-sinbxÉè¶þ´Î...


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ÈçºÎÖ¤Ã÷int_0^¡Þ(sinax/sinbx)(dx/(x^2+¦Â^2))£¿integration - Is there a non-trivial definite integral that values to $\frac{e...


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Çó¼«ÏÞx➔0lim[e^(ax)-e^(bx)]/(sinax-sinbx)½â£ºÔ­Ê½=x➔0lim[e^(ax)-e^(bx)]/(ax-bx)=x➔0lim[ae^(ax)-be^(bx)]/(a-b...


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