设数列xn有界+又limyn+0

薛咸胖2724又是数列问题设数列{Xn}有界,又limYn=0,证明:limXnYn=0 -
叔音看13291946219 ______[答案] 无穷小乘以有界量等于无穷小.

薛咸胖2724设数列{Xn}有界,又limYn=0,n - >无穷大,证明limXnYn=0,n - >无穷大 -
叔音看13291946219 ______[答案] 因为数列{Xn}有界 所以不妨假设|Xn|0) 因为数列{Yn}的极限是0 则对于任意给出的e,总存在N,使得n>N时,|Yn|N的时候|XnYn|=|Xn||Yn|

薛咸胖2724设数列Xn有界有limyn=0证明limxnyn=0 -
叔音看13291946219 ______[答案] let |xn| ≤M -M ≤ xn ≤ M -Mlim(n->∞)yn ≤lim(n->∞)xnyn ≤ Mlim(n->∞)yn 0 ≤lim(n->∞)xnyn ≤ 0 lim(n->∞)xnyn =0

薛咸胖2724设数列{Xn}有界,且limYn=0.证明limYnXn=0. -
叔音看13291946219 ______[答案] xn有界,所以存在M>0,|xn|0,当n>N时,有|yn|0,当n>N,|xnyn|

薛咸胖2724收敛数列的有界性问题设数列{Xn}有界,又lim Yn=0,证明:lim XnYn=0.囧么办?111 -
叔音看13291946219 ______[答案] |xn|≤M -Myn≤xn.yn≤Myn -Mlim(n->∞)yn≤lim(n->∞)xn.yn≤Mlim(n->∞)yn 0 ≤lim(n->∞)xn.yn≤0 =>lim(n->∞)xn.yn =0

薛咸胖2724急!大一微积分题目,学长请进1.设数列{Xn}有界,又limyn=0 证明:lim Xn·yn=0 n→+∞ n→+∞2设数列{Xn}有界,若X 2k - 1→a(k→∞),X 2k→a(k→∞),证明lim... -
叔音看13291946219 ______[答案] 1. 设 M>0, |x(n)| ≤ M. limy(n)=0 => 任给ε>0, 存在正整数N,使得当n>N 时,总有 | y(n) - 0 | < ε/M 此时 | x(n) y(n) - 0 | ≤ M |y(n)| < ε 即证 lim x(n) y(n) =0 2. 见图片 3. {sin(nπ/2)} = { 1,0,-1,0, 1,0,-1,0, . } 取 {sin (nπ/2)} 的两个子列: { 1, 1, 1, 1, . } 和 {0,0,0,...

薛咸胖2724设数列|xn| 有界,又limyn=0 n趋向无穷,证明limxnyn=0 n趋向无穷 -
叔音看13291946219 ______ 设|xn|上确界为sup|xn| lim xnyn <=(小于等于)lim|xn|yn <=lim sup|xn|yn = sup|xn|*lim yn = sup|xn|*0=0 同理 lim xnyn >=(大于等于)lim -|xn|yn >=lim -sup|xn|yn = 0 即 0<=lim xnyn<=0 limxnyn=0 n趋向无穷 证毕

薛咸胖2724题目:设数列{Xn}有界,又lim(n - >正无穷)Yn=0,证明:lim(n - >正无穷)XnYn=0.要详细的过程,定义法 -
叔音看13291946219 ______ 如果存在M>0,对任意的n都有:|xn|≤M,称数列{xn}有界.所以lim(n->正无穷) Xn=M 故lim(n->正无穷)XnYn=[lim(n->正无穷)Xn]*[lim(n->正无穷)Yn]=M*0=0

薛咸胖2724设数列{Xn}有界,又limYn=0,证明:limXnYn=0 -
叔音看13291946219 ______ 数列Xn有界,即!Xn!<=M恒成立.limYn=0,即对任意E>0,总有N>0使得当n>N时!Yn-0!<E恒成立.而!Xn!*!Yn-0!=!XnYn-0!所以对任意ME>0,总有N>0使得当n>N时!XnYn-0!<ME恒成立.所以limXnYn=0

薛咸胖2724设数列{x(n)}有界,又lim x(n)(n趋近无限大)=0.证明:lim x(n)y(n)(n趋近无限大)=osorry,是lim y(n)(n趋近无限大)=0 -
叔音看13291946219 ______[答案] 因为{y(n)}有界则得,|y(n)|又因为lim x(n)(n趋近无限大)=0. 即存在N(ε)>0,使n>N时,有lim x(n)(n趋近无限大)则当x>N时,|limx(n)y(n)(n趋近无限大)|把x,y互换即可