求下列极限 lim{n[ln(n+2)-lnn]}趋向于无穷 lim ln(1+2x)/sin3x趋向于0

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求下列极限 lim{n[ln(n+2)-lnn]}趋向于无穷 lim ln(1+2x)/sin3x趋向于0
求下列极限 lim{n[ln(n+2)-lnn]}趋向于无穷 lim ln(1+2x)/sin3x趋向于0

求下列极限 lim{n[ln(n+2)-lnn]}趋向于无穷 lim ln(1+2x)/sin3x趋向于0
lim{n[ln(n+2)-lnn]}=limln{[(n+2)/n]^n}=limln[(1+2/n)^n]=2limln[(1+2/n)^(n/2)]=2lne=2
lim ln(1+2x)/sin3x分子分母同时分别求导得
lim ln(1+2x)/sin3x= lim{ [2/(1+2x)]/3cos3x}=2/3

lim{n[ln(n+2)-lnn]}趋向于无穷
=lim ln(1+2/n)^(n/2)*2
=lim 2ln[(n+2)/n]^n/2
=2
lim ln(1+2x)/sin3x趋向于0
=lim ln(1+2x)/3x
=lim ln(1+2x)^(2/x) *1/6
=1/6