1.原式=lim(x->无穷)(1+sinx/x)
=lim(x->无穷)(1+0)
=1
说明:1/x为无穷小量,sinx为有界函数,定理:有界函数与无穷小量乘积是无穷小量.
2.原式=lim(x->0)[x/sinx*x+W]
=lim(x->0)[1*x+W]
=0+W
说明:定理:lim(x->0)x/sinx=1,
W无极限,W为有界函数sin1/x与无穷大量1/sinx的积,无极限值.
3.原式=0+有界函数,无极限.
1.原式=lim(x->无穷)(1+sinx/x)
=lim(x->无穷)(1+0)
=1
说明:1/x为无穷小量,sinx为有界函数,定理:有界函数与无穷小量乘积是无穷小量.
2.原式=lim(x->0)[x/sinx*x+W]
=lim(x->0)[1*x+W]
=0+W
说明:定理:lim(x->0)x/sinx=1,
W无极限,W为有界函数sin1/x与无穷大量1/sinx的积,无极限值.
3.原式=0+有界函数,无极限.