Take 15 minutes to prepare this exercise.
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Question
Find the Taylor-expansion of order 4 of the following applications:
a)
b)
c)
a) Replace
by its Taylor-expansion of order
, simplify by
then use the Taylor-expansion of application
b) Replace
by its Taylor-expansion of order
then use the Taylor-expansion of application
c) Replace
by its Taylor-expansion of order
then put the obtained expression in the form
and use the Taylor-expansion of application
a) Using the Taylor-expansion of order
of application
we have:
Using the Taylore-expansion of
with
we obtain:
b)
We then use the Taylor-expansion of
with
c)
We then use the Taylor-expansion of
avec
