(tanx)^[1/(cosx-sinx)]当x趋于π/4时,求极限
问题描述：
(tanx)^[1/(cosx-sinx)]当x趋于π/4时,求极限
答
原式=lim(x趋于π/4）e^[lntanx/(cosx-sinx)] …………分子分母同时趋于0,罗必达法则
=lim(x趋于π/4）e^[(1/cos^2xtanx)/(-sinx-cosx)]
=lim(x趋于π/4）e^1/[-sinxcosx(sinx+cosx)]
=e^(-√2)