当x趋向于0+时,limln(sin3x)/ln(sinx)的极限

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当x趋向于0+时,limln(sin3x)/ln(sinx)的极限
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当x趋向于0+时,limln(sin3x)/ln(sinx)的极限
当x趋向于0+时,limln(sin3x)/ln(sinx)的极限

当x趋向于0+时,limln(sin3x)/ln(sinx)的极限
lim(x→0+) ln(sin3x)/ln(sinx)
=lim(x→0+) [3cos3x/(sin3x)/[cosx/sinx]
=lim(x→0+) (3sinx/sin3x=1

罗比达法则：
=lim3[cos3x/sin3x]/[cosx/sinx]
=lim3sinx/sin3x=1

lim(x→0+) ln(sin3x)/ln(sinx)
=lim(x→0+) (sinx)'/(sin3x)'
=lim(x→0+) cosx/(3cos3x)
=1/3