1 lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向无穷)2 lim(1/x-1/sinx) 利用泰勒公式求极限(n趋向0)
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1lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向无穷)2lim(1/x-1/sinx)利用泰勒公式求极限(n趋向0)1lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向
1 lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向无穷)2 lim(1/x-1/sinx) 利用泰勒公式求极限(n趋向0)
1 lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向无穷)
2 lim(1/x-1/sinx) 利用泰勒公式求极限(n趋向0)
1 lim(n+1/2)In(1+1/n)利用泰勒公式求极限(n趋向无穷)2 lim(1/x-1/sinx) 利用泰勒公式求极限(n趋向0)
如图:
lim(n趋向无穷)(n+1/2)In(1+1/n)=lim(n趋向无穷)[nIn(1+1/n)+(1/2)In(1+1/n)
=lim(n趋向无穷){[In(1+1/n)^n]+(1/2)In(1+1/n)}=lim(n趋向无穷)[In(1+1/n)^n]+lim(n趋向无穷)(1/2)In(1+1/n)
=e+(1/2)lim(n趋向无穷)In(1+1/n)=e+0=e,
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lim(n趋向无穷)(n+1/2)In(1+1/n)=lim(n趋向无穷)[nIn(1+1/n)+(1/2)In(1+1/n)
=lim(n趋向无穷){[In(1+1/n)^n]+(1/2)In(1+1/n)}=lim(n趋向无穷)[In(1+1/n)^n]+lim(n趋向无穷)(1/2)In(1+1/n)
=e+(1/2)lim(n趋向无穷)In(1+1/n)=e+0=e,
若利用泰勒公式,In(1+1/n)=1/n+o(1/n),
lim(n趋向无穷)In(1+1/n)=lim(1/n趋向0)[1/n+o(1/n)]=0
利用泰勒公式求极限
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