Step 1:
\\
\
The function is
\
\
\
Find the successive differentiation of
.
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\

\
\
\
\
\
\
\
Centered at
.
\
\
\
\
\
\
\

\
\
\
\
\
\
\
\
\
\
\
\
\
\

\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
Step 2:
\\
\
\
\
\
\
\
Definition of Taylor series:
\\
\
\
\
\
\
\
If a function
has derivatives of all orders at
then the series
\
\
\
\
\
is called Taylor series for
at
.
Find the Taylor series for
.
\
\
\
\
\
\
\
\
\
Substitute the above values in Taylor series.
\\
\
\
\
\
\
\

\
\
\
\
\
\
\

\
\
\
\
\
\
\
.sollution:
Taylor series of
is
.