已知lim x趋近于0 (1-4x)的(1-x)/x次方

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已知lim x趋近于0 (1-4x)的(1-x)/x次方

已知lim x趋近于0 (1-4x)的(1-x)/x次方
已知lim x趋近于0 (1-4x)的(1-x)/x次方

已知lim x趋近于0 (1-4x)的(1-x)/x次方
lim x趋近于0 (1-4x)的(1-x)/x次方
=e^[lim x趋近于0 [-4x (1-x)/x]
=e^[lim x趋近于0 [-4 (1-x)]
=e^(-4)

L =lim(x->0) (1-4x)^[(1-x)/x]
lnL = lim(x->0) xln(1-4x)/ (1-x) (0/0)
=lim(x->0) [ 4x/(1-4x) - ln(1-4x) ]
= 0
L =e