作业帮求Lim(x→0)(sinx/x)^(cosx/1-cosx)
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求Lim(x→0)(sinx/x)^(cosx/1-cosx)
求Lim(x→0)(sinx/x)^(cosx/1-cosx)
求Lim(x→0)(sinx/x)^(cosx/1-cosx)
y=(sinx/x)^(cosx/1-cosx)
lny=(cosx(lnsinx-lnx)/(1-cosx)
limlny=lim(cosx(lnsinx-lnx)/(1-cosx)=lim(lnsinx-lnx)/(1-cosx)=lim(cosx/sinx-1/x)/sinx=lim(xcosx-sinx)/x^3=lim(cosx-xsinx-cosx)/3x^2=-1/3
limy=e^(-1/3)
L=lim(x→0)(sinx/x)^(cosx/(1-cosx))
lnL = lim(x→0)(1-cosx)ln(sinx/x)/(cosx)
=0
L= 1
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