如果指數(shù)是1/ln(2+x^2)的話,則指數(shù)極限是1/ln2；底數(shù)極限是1,結(jié)果是1.
如果指數(shù)是1/ln(1+x^2)的話,則
極限=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 ,則x=sinu.
當x趨向0時,ux趨向0
則原極限=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)