- E39
[1FJ] Write the Taylor polynomial of \(f(x)\) around \(x_ 0=0\), using ”Landau’s calculus of \(o(x^ n)\)” seen above.
\(f(x)\)
=
\(p(x) + o(x^ 4)\)
\((\cos (x))^ 2\)
=
\(+o(x^ 4)\)
\((\cos (x))^ 3\)
=
\(+o(x^ 4)\)
\(\cos (x)e^ x\)
=
\(+o(x^ 4)\)
\(\cos (\sin (x))\)
=
\(+o(x^ 4)\)
\(\sin (\cos (x))\)
=
\(+o(x^ 4)\)
\(\log (\log (e+x))\)
=
\(+o(x^ 3)\)
\((1+x)^{1/x}\)
=
\(+o(x^ 3)\)
(A little imagination is required to address the last two. To reduce the computations, develop the last two only up to \(o(x^ 3)\)).
Solution 1
EDB — 1FJ
View
English
Authors:
"Mennucci , Andrea C. G."
.
Managing blob in: Multiple languages