lim(x趋于0)(tanx-sinx)/3x^2
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lim(x趋于0)(tanx-sinx)/3x^2
0/0型,用洛比达法则,
lim(x趋于0)(tanx-sinx)/(3x^2)=lim(x趋于0)(tanx-sinx)'/(3x^2)'=lim(x趋于0)[(tanx)'-(sinx)']/(6x)
=lim(x趋于0)[1/(cosx)^2-cosx]/(6x)==lim(x趋于0)[1/(cosx)^2-cosx]'/(6x)'
=lim(x趋于0){[1/(cosx)^2]'-(cosx)'}/6=lim(x趋于0)[(2sinx)/(cosx)^3+sinx]/6=[(2sin0)/(cos0)^3+sin0]/6=0
lim(x趋于0)(tanx-sinx)/(3x^2)=lim(x趋于0)(tanx-sinx)'/(3x^2)'=lim(x趋于0)[(tanx)'-(sinx)']/(6x)
=lim(x趋于0)[1/(cosx)^2-cosx]/(6x)==lim(x趋于0)[1/(cosx)^2-cosx]'/(6x)'
=lim(x趋于0){[1/(cosx)^2]'-(cosx)'}/6=lim(x趋于0)[(2sinx)/(cosx)^3+sinx]/6=[(2sin0)/(cos0)^3+sin0]/6=0
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