Question

Use Taylors Inequality to estimate the accuracy of the approximation
f(x)≈Tn(x)
0.8≤x≤1.2
\[sin(1)+cos(1)(x-1)-\frac{sin(1)(x-1)^2}{2}-\frac{cos(1)(x-1)^3}{6}\]
when x lies in the given interval

Answer 1

so far we know that
\[\left|R_n(x) \right|=\left|f(x)-T_n(x)\right|\]

Answer 2

and we also know that
if
\[\left|f^{(n+1)}(x)\right|\le M\]
then
\[\left|R_n(x) \right|\le \frac{M}{(n+1)!}\left| x-a\right|^{n+1}\]

Answer 3

is the first term is sin1 or sin t?

Answer 4

the original equation is f(x)= sinx
a=1
and n=3

Answer 5

oh I thought wrong that were coff !!