lim(sin x+cos x)^（1／X）(X趋近于零）

lim(x->0) (sin x+cos x)^（1／x)
=lim(x->0) e^ {ln[(sin x+cos x)^（1／x)]}
=lim(x->0) e^ {ln[(sin x+cos x)}/x
= e^lim(x->0) {ln[(sin x+cos x)}/x
= e^lim(x->0) {(cosx-sinx)/(sin x+cos x)}/1
= e^{(1-0)/(0+1)}
= e^1