# Taylor Polynomial for e^x

• March 8th 2011, 01:37 PM
zebra2147
Taylor Polynomial for e^x
I could really use some help with the following...Any guidance or hints are appreciated.

Let $f(x) := e^x.$
Show that the nth Taylor polynomial for $f$ at 0 is
$T_nf(x) =\sum_{k=0}^{n}\frac{x^k}{k!}$
and the Lagrange Remainder is
$R_nf(x) = e^c\frac{x^{n+1}}{(n + 1)!}$ for some c between 0 and x.
• March 8th 2011, 02:02 PM
Bruno J.
This is just a straightforward application of Taylor's theorem, using the fact that $(e^x)'=e^x$ and $e^0=1$.