作业帮高数的无穷小的比较.
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/09 08:36:52
高数的无穷小的比较.
用等价无穷小替换可注意到
ln(1+t) t ,e^t - 1 t (t→0),
有
2）g.e.= lim(x→0)[(3sinx)/x]*lim(x→0)[1/(1+cosx)]
+ lim(x→0)[(x^2)cos(1/x)/x]*lim(x→0)[1/(1+cosx)]
= 3lim(x→0)(sinx/x)*lim(x→0)[1/(1+cosx)]
+ lim(x→0)[xcos(1/x)]*lim(x→0)[1/(1+cosx)]
= 3*(1/2) + 0*1
= 3/2.
3）g.e.= lim(x→0)(-sin2x)/(3x) = -2/3.
ln(1+t) t ,e^t - 1 t (t→0),
有
2）g.e.= lim(x→0)[(3sinx)/x]*lim(x→0)[1/(1+cosx)]
+ lim(x→0)[(x^2)cos(1/x)/x]*lim(x→0)[1/(1+cosx)]
= 3lim(x→0)(sinx/x)*lim(x→0)[1/(1+cosx)]
+ lim(x→0)[xcos(1/x)]*lim(x→0)[1/(1+cosx)]
= 3*(1/2) + 0*1
= 3/2.
3）g.e.= lim(x→0)(-sin2x)/(3x) = -2/3.