当n趋向于x时数列1/n.cosnx的极限

Question

当n趋向于x时 数列1/n.cosnx的极限

Answer 1

x不为0且x为有限值时,lim_{n->x}cos(nx)/n = cos(x^2)/x,
x为无穷大时,|cos(nx)|0为无穷小.有界乘无穷小,还是无穷小,极限为0.
x=0时,cos(nx)=cos(0)=1,1/n->无穷大,极限为无穷大.