用洛必达法则求下列极限(1)lim(x→0^＋)lntan7x/lntan2x(2)lim(x→0)xcot2x
网友回答
(1)lim(x→0^＋)lntan7x/lntan2x
=lim [7(sec7x)^2 / tan7x ] / [2(sec2x)^2 / tan2x ]
=lim [7(sec7x)^2 *tan2x] / [2(sec2x)^2* tan7x ] 罗比达法则
=lim [7(sec7x)^2 *2x] / [2(sec2x)^2* 7x ] 等价替换
lim [7 *2] / [2* 7 ] =1
(2)lim(x→0)xcot2x
=lim[ x*cos 2x]/sin2x
=limx/sin2x 罗比达法则
=lim1/2cos2x
=1/2======以下答案可供参考======
供参考答案1:
1.=12.=1/2