lim【x→0+】(1-cosx)^(1/lnx)

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lim【x→0+】(1-cosx)^(1/lnx)
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lim【x→0+】(1-cosx)^(1/lnx)
lim【x→0+】(1-cosx)^(1/lnx)

lim【x→0+】(1-cosx)^(1/lnx)
y=(1-cosx)^(1/lnx)
lny=(1/lnx)ln(1-cosx)=(x²/2)/lnx =x²/(2lnx)
lim【x→0+】lny
=lim【x→0+】x²/(2lnx)
=lim【x→0+】(2x)/(2/x)
=lim【x→0+】x²
=0
故lim【x→0+】=1

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