## cherrilyn 5 years ago Let Tn(x) be the Taylor Polynomial for f(x) = lnx at a=1 and c>1........

1. cherrilyn

Show that the max of $f ^{(k+1)}(x) on [1,c] is f^{(k+1)}(1)$

2. cherrilyn

Prove $\left| T _{n}(c)-\ln c \right|\le \left| (c-1 \right|^ {n+1})/(n+1)$

3. cherrilyn

and Find n such that $\left| T _{n}(1.5)-\ln 1.5 \right| \le 10^{-2}$

4. anonymous

the first one is easy the f(k+1) derivative will be

5. anonymous

$A*(1/x)^{k+1}$ This is a decreaing function, so the maximum on $\left[ 1,c \right]$ will be1.