求极限 如图 20
1个回答
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(16)
lim(x->+∞) x[ln(x+1) -lnx ]
=lim(x->+∞) ln[(x+1)/x]^x
=ln( lim(x->+∞)[(x+1)/x]^x )
=ln[ lim(x->+∞)(1 + 1/x)^x ]
=lne
=1
(18)
let
2/(2x+1) =1/y
x= (2y-1)/2
lim(x->+∞)[ (2x+3/(2x+1)]^(x+1)
=lim(x->+∞)[ 1 + 2/(2x+1) ]^(x+1)
=lim(y->+∞)[ 1 + 1/y ]^[ (2y-1)/2+1 ]
=lim(y->+∞)[ 1 + 1/y ]^y
=e
lim(x->+∞) x[ln(x+1) -lnx ]
=lim(x->+∞) ln[(x+1)/x]^x
=ln( lim(x->+∞)[(x+1)/x]^x )
=ln[ lim(x->+∞)(1 + 1/x)^x ]
=lne
=1
(18)
let
2/(2x+1) =1/y
x= (2y-1)/2
lim(x->+∞)[ (2x+3/(2x+1)]^(x+1)
=lim(x->+∞)[ 1 + 2/(2x+1) ]^(x+1)
=lim(y->+∞)[ 1 + 1/y ]^[ (2y-1)/2+1 ]
=lim(y->+∞)[ 1 + 1/y ]^y
=e
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