lim(n→∞)[1-(2n/n+3)]

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lim(n→∞)[1-(2n/n+3)]
lim(n→∞)[1-(2n/n+3)]

lim(n→∞)[1-(2n/n+3)]
lim(n→∞)[1-(2n/n+3)]
=1-lim(n→∞)(2n/n+3)
=1-lim(n→∞)[2/[1+(3/n)]
=1-2=-1

导数??
-6/(n^2+6n+9)

lim(n→∞)[1-2n/(n+3)]
=-1

解法一:lim(n→∞)[1-2n/(n+3)]=lim(n→∞)[1-2/(1+3/n)]
=1-2/(1+0)
=-1;
解法二(定义法):∵对任意的ε>0,取N=[6/ε] ([6/ε]表示不超过6/ε的最大整数)
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解法一:lim(n→∞)[1-2n/(n+3)]=lim(n→∞)[1-2/(1+3/n)]
=1-2/(1+0)
=-1;
解法二(定义法):∵对任意的ε>0,取N=[6/ε] ([6/ε]表示不超过6/ε的最大整数)
当n>N时,有|1-2n/(n+3)-(-1)|=6/(n+3)<6/n<ε
∴根据极限定义知 lim(n→∞)[1-2n/(n+3)]=-1.

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