计算极限limx→0∫(上限x,下限x^2)tantdt/1-cosx

问题描述:

计算极限limx→0∫(上限x,下限x^2)tantdt/1-cosx

lim(x-->0) [∫(x²~x) tant dt]/(1 - cosx)
= lim(x-->0) (tanx - 2xtanx²)/sinx 0) (sinx/cosx - 2xtanx²)/sinx
= lim(x-->0) (1/cosx - x/sinx * 2tanx²)
= 1 - 1 * 0
= 1