- #1
yupenn
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Taylor's Inequality states:
if |f n+1(x)|<=M
then
|Rn(x)|<=M*|x-a|^(n+1)/(n+1)!
however,
Rn(x)=f n+1(x)*|x-a|^(n+1)/(n+1)!+...
it seems |Rn(x)|>=M*|x-a|^(n+1)/(n+1)! when |f n+1(x)|=M
the inequality is wrong??
if |f n+1(x)|<=M
then
|Rn(x)|<=M*|x-a|^(n+1)/(n+1)!
however,
Rn(x)=f n+1(x)*|x-a|^(n+1)/(n+1)!+...
it seems |Rn(x)|>=M*|x-a|^(n+1)/(n+1)! when |f n+1(x)|=M
the inequality is wrong??