如果指数是1/ln(2+x^2)的话,则指数极限是1/ln2；底数极限是1,结果是1.
如果指数是1/ln(1+x^2)的话,则
极限=e^lim( (1/ln(1+x^2)) ·ln(aresinx/x) )
=e^lim( ln(aresinx/x) / ln(1+x^2) )
=e^lim( ln(1+ aresinx/x -1) / ln(1+x^2) )
=e^lim( ( aresinx/x -1) / (x^2) )
=e^lim( ( aresinx -x) / (x³) )
令u=aresinx ,则x=sinu.
当x趋向0时,ux趋向0
则原极限=e^lim((u-sinu)/(sin³u) )
=e^lim( (u-sinu)/(u³) )
=e^lim( (1-cosu)/(3u²) )
=e^lim( (1/2)u²)/(3u²) )
=e^lim(1/6)