ln(1+t)=t-t^2/2+o(t^2)
cost=1-t^2/2+o(t^2)
1-cost=t^2/2+o(t^2)
所以,
原式=lim(t→0)[t^2/2+o(t^2)]/[t-t^2/2+o(t^2)]
=lim(t→0)[t^2/2]/[t-t^2/2]
=lim(t→0)[t/2]/[1-t/2]
=0
【附注】ln(1+t)=t-t^2/2+o(t^2)
可以看到,ln(1+t)是t的一阶无穷小,要注意了!
ln(1+t)=t-t^2/2+o(t^2)
cost=1-t^2/2+o(t^2)
1-cost=t^2/2+o(t^2)
所以,
原式=lim(t→0)[t^2/2+o(t^2)]/[t-t^2/2+o(t^2)]
=lim(t→0)[t^2/2]/[t-t^2/2]
=lim(t→0)[t/2]/[1-t/2]
=0
【附注】ln(1+t)=t-t^2/2+o(t^2)
可以看到,ln(1+t)是t的一阶无穷小,要注意了!