求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)
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求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)求lim(x->&无穷)sinn/n,求lim(
求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)
求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)
求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n)
答:
是n趋向于无穷吧,变量中没有x.
1.
lim(n->∞)(sinn)/n
分子sinn有界,即|sinn|<=1,而分母趋向无穷大,所以(sinn)/n=0
2.
lim(n->∞)sin(1/n)
当n->∞时,1/n=0
sin0=0
所以lim(n->∞)sin(1/n)=0
或者可以这样算:
lim(n->∞)sin(1/n)
=lim(n->∞)(sin(1/n)/(1/n))*(1/n)
当n->∞时,1/n=0,sin(1/n)/(1/n)=1(重要极限)
所以=lim(n->∞)(sin(1/n)/(1/n))*(1/n)
==lim(n->∞) 1/n=0
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