几道极限高数题,1.lim (e^x^2-1)/(x^2-sinX) …… ……2.lim（2sinx-sin2x)/x
4个回答
1.lim (e^x^2-1)/(x^2-sinX)=limx^2/(x^2-sinx).(等价无穷小代换e^x^2-1~x^2)
=limx^2/(-sinx).(等价无穷小代换x^2-sinx~-sinx)
=-limx*limx/sinx
=0
2.lim（2sinx-sin2x)/x^3=lim（2sinx-2sinxcosx)/x^3
=lim[2sinx(1-cosx)]/x^3
=2lim[x*(1/2)x^2]/x^3.(等价无穷小代换x~sinx,1-cosx~(1/2)x^2)
=1
3.lim(e^x^2-cosx)/ln(1+x^2)=lim(e^x^2-cosx)/x^2.(等价无穷小代换ln(1+x^2)~x^2)
=lim(e^x^2-1+1-cosx)/x^2
=lim(e^x^2-1)/x^2+lim(1-cosx)/x^2
=limx^2/x^2+lim(1/2)x^2/x^2.(等价无穷小代换e^x^2-1~x^2,
1-cosx~1/2x^2)
=1+1/2
=3/2
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