lim(x+e^3x)^1/x
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lim(x+e^3x)^1/x
lim(x+e^3x)^1/x
lim(x+e^3x)^1/x
应该是x→0吧
这是1^∞型极限,可用重要极限lim(x→0) (1+x)^(1/x)=e
lim(x→0) [x+e^(3x)]^(1/x)
=lim(x→0) [1+x+e^(3x)-1]^(1/x)
=lim(x→0) [1+x+e^(3x)-1]^{[1/(x+e^(3x)-1)]*[(x+e^(3x)-1]/x}
=e^ lim(x→0) [(x+e^(3x)-1]/x
=e^ lim(x→0) 1+3e^(3x)
=e^4
lim(x+e^3x)^1/x,这里x趋近于零,
原式=lim[1+(x+e^3x-1)]^1/x=lim[1+(x+e^3x-1)]^[1/(x+e^3x-1)](x+e^3x-1)1/x=lime^(x+e^3x-1)/x=e^4
lim(x+e^3x)^1/x
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