lim(sin2x/x)^(1+3x),当x趋于0时等于多少
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lim(sin2x/x)^(1+3x),当x趋于0时等于多少
lim(sin2x/x)^(1+3x),当x趋于0时等于多少
lim(sin2x/x)^(1+3x),当x趋于0时等于多少
lim(x→0)(sin2x/x)^(1+3x)
=lim(x→0)(sin2x/x)^[lim(x→0)(1+3x)]
=lim(x→0)(sin2x/x)^1
=lim(x→0)(sin2x/x)
=2
也可以这样
lim(x→0)(sin2x/x)^(1+3x)
=lim(x→0)(sin2x/(2x))^(1+3x) *2^(1+3x)]
lim(2x→0)(sin2x/2x)=1
=1*2
=2
lim(x→0)(sin2x/x)^(1+3x)
=lim(x→0)e^[(1+3x)ln2(sin2x/2x)]
=e^lim(x→0)(1+3x)ln2(sin2x/2x)
=e^(1*ln2)
=2
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