lim(x趋于-1)(sin(x+1))⼀2(x+1)

2025-06-25 03:20:36
推荐回答(1个)
回答1:

分子分母同趋于0可用洛必达法则
lim(x趋于-1)(sin(x+1))/2(x+1)
=
lim(x趋于-1)(sin(x+1))'/(2(x+1))'
=
lim(x趋于-1)(cos(x+1))/2
= cos0/2
= 1/2
如果没学过洛必达法则,可以用不等式逼近
x在一定范围内有
x/(x+1)