【羅必塔法則】
lim(x->0) [√(1-x^2)]^(1/x)
=lim(x->0) e^{ (1/x)ln[√(1-x^2)] }
=lim(x->0) e^{ 1/2 ln(1-x^2) /x }
= e^ { 1/2*lim(x->0)[ln(1-x^2)/x] }
羅必塔法則
= e^{ 1/2*lim(x->0) [(-2x)/(1-x^2) /1 ]}
= e^0
= 1
【重要極限其實(shí)更簡潔】
lim(x->0) [(1-x^2)^(1/2)]^(1/x)
=lim(x->0) [1+(-x^2)]^(1/2x)
=lim(x->0) {[1+(-x^2)]^(-1/x^2)}^(-x/2)
= e^0
= 1