Question

用洛毕达法则求极限limlntan7x/lntan2x(x趋于0+)

第二步到第三步怎么化的

Answer 1

lim(x->0+) ln(tan7x)/ln(tan2x)

洛必达

lim(x->0+) [7(sec7x)^2/(tan7x)]/[2(sec2x)^2/(tan2x)]

=(7/2)lim(x->0+) tan2x/tan7x

=(7/2)lim(x->0+) 2x/(7x)

=1