(1)åæ¯â0ï¼æéåå¨ï¼ååâ0,0/0ï¼ç¨æ´å¿
è¾¾æ³å
â´åå¼=lim(xâ0)(1+sin2x)/1=1
(2)=lim(xâ0)arcsinx/2x=lim(xâ0)1/2â(1-x²)=½
(3)=lim(xâ0)(1-e^x²)/(2xsin2x+2x²cos2x)
=lim(xâ0)(-2xe^x²)/(2sin2x+4xcosx+4xcos2x-4x²sin2x)
=lim(xâ0)(-e^x²)/(2sin2x/2x+4cosx-2xsin2x)
âµlim(xâ0)sin2x/2x=1
â´åæé=-1/6
(4)为â/âç¨æ´å¿
è¾¾æ³å
=lim(xâ+â)[2â«(0,x)e^u²du)·e^x²]/e^2x²
=lim(xâ+â)[2â«(0,x)e^u²du)]/e^x²
=lim(xâ+â)[2e^x²)]/2xe^x²
=lim(xâ+â)2/2x
=0
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