(tanx)^[1/(cosx-sinx)]当x

题目

(tanx)^[1/(cosx-sinx)]当x

答案

洛必达法则
原式=lim(x趋于π/4）e^[lntanx/(cosx-sinx)]
=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)