x趋近0时,求lim(1+2x)^(1/sinx)
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x趋近0时,求lim(1+2x)^(1/sinx)
lim[x→0] (1+2x)^(1/sinx)
=lim[x→0] (1+2x)^[(1/2x)*(2x/sinx)]
=lim[x→0] [(1+2x)^(1/2x)] ^2(x/sinx)
=e^2
=lim[x→0] (1+2x)^[(1/2x)*(2x/sinx)]
=lim[x→0] [(1+2x)^(1/2x)] ^2(x/sinx)
=e^2
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