作业帮证明极限存在,并求极限
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/14 05:12:31
证明极限存在,并求极限
|x(n+1)|=|sin(xn)| ≤1
x(n+1)=sin(xn) < xn
xn is decreasing
=> lim(n->∞)xn exists
let lim(n->∞)xn =L
lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
L = sinL
L =0
再问： lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
怎么得到
L = sinL
再答： x(n+1) =sinxn
lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
L = sinL
x(n+1)=sin(xn) < xn
xn is decreasing
=> lim(n->∞)xn exists
let lim(n->∞)xn =L
lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
L = sinL
L =0
再问： lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
怎么得到
L = sinL
再答： x(n+1) =sinxn
lim(n->∞)x(n+1)=lim(n->∞)sin(xn)
L = sinL