大一高数 lim xsin[ln(1+3/x)](x趋向无穷大)=?大一高数lim xsin[ln(1+3/x)](x趋向无穷大)=?
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大一高数 lim xsin[ln(1+3/x)](x趋向无穷大)=?大一高数lim xsin[ln(1+3/x)](x趋向无穷大)=?
大一高数 lim xsin[ln(1+3/x)](x趋向无穷大)=?
大一高数
lim xsin[ln(1+3/x)](x趋向无穷大)=?
大一高数 lim xsin[ln(1+3/x)](x趋向无穷大)=?大一高数lim xsin[ln(1+3/x)](x趋向无穷大)=?
ln(1+3/x)=ln [(1+3/x)^(x/3)]^(3/x)
=3/x ln(1+3/x)^(x/3)
lim xsin[ln(1+3/x)] (x趋向无穷大)
=lim x sin[3/x ln(1+3/x)]^(x/3)] (x趋向无穷大)
=lim xsin(3/x) (x趋向无穷大)
=lim 3 sin(3/x) /(3/x)
=3
in(1+3/x)在x无限大时约等于3/x(课本上面有推论,自己去看)
所以式子就化成了x*3/x