Question

x趋向于无穷大时lim(1+k/x)^x 如何用洛必达法则求解

Answer 1

x趋向于无穷大时lim(1+k/x)^x

=e^lim(x->∞)ln(1+k/x)/(1/x)

令1/x=t,则t->0

原式=e^lim(t->0)ln(1+kt)/t

=e^lim(t->0)k/(1+kt)/1

=e^k