关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=3/2 3.lim2^n/n!=0第一题中ξ=0.1,0.01,0.001时的N值要怎么求呢!
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![关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=3/2 3.lim2^n/n!=0第一题中ξ=0.1,0.01,0.001时的N值要怎么求呢!](/uploads/image/z/5096026-10-6.jpg?t=%E5%85%B3%E4%BA%8E%E9%AB%98%E6%95%B0%E6%9E%81%E9%99%90%E8%AF%81%E6%98%8E%E7%9A%84%E5%87%A0%E9%81%93%E9%A2%98+%E8%AF%81%E6%98%8E+1.lim%28xn%29%3Dn%5E2%2F%282n%5E3%2B1%29%3D0+2.lim%283n%2B1%29%2F%282n-1%29%3D3%2F2+3.lim2%5En%2Fn%21%3D0%E7%AC%AC%E4%B8%80%E9%A2%98%E4%B8%AD%CE%BE%3D0.1%2C0.01%2C0.001%E6%97%B6%E7%9A%84N%E5%80%BC%E8%A6%81%E6%80%8E%E4%B9%88%E6%B1%82%E5%91%A2%21)
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关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=3/2 3.lim2^n/n!=0第一题中ξ=0.1,0.01,0.001时的N值要怎么求呢!
关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=3/2 3.lim2^n/n!=0
第一题中
ξ=0.1,0.01,0.001时的N值要怎么求呢!
关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=3/2 3.lim2^n/n!=0第一题中ξ=0.1,0.01,0.001时的N值要怎么求呢!
1、limn^2/(2n^3 +1) =lim(1/n) / (2 + 1/n^3)
∵n→∞时,1/n→0,1/n^3 →0
所以原式=0
2、lim(3n+1)/(2n-1) = lim(3+ 1/n) / (2- 1/n) = 3/2
3、2^n/n!= 2^n/(1*2*3*...*n) < 2^n/(1*2*3*3*3...*3) = 2*(2/3)^(n-2)
所以0
证明: 1’ 当n=1时,左= (2*1-1) 2; =1, 右=1/3*1*(4*1 2’ 假设当 n=k时,命题成立 即1 2; 3 2; 5 2; (2k-1)
放缩法n^2/(2n^3+1)小于n^2/(2n^3)