Take 10 minutes to prepare this exercise.
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A detailed solution is then proposed to you.
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Question
a) Using the Taylor-expansion of order
of application
find the Taylor-expansion of order
around
of application
b) By integrating the previous Taylor-expansion, find the Taylor-expansion of order
around
of function
a) Write the Taylor-expansion of application
then replace
by
b) Check that the integration constant is zero.
a)
By substituing
to
we obtain:
b) By integrating the previous Taylor-expansion, we infer:
By giving to
the zero value, we notice that the integration constant is zero, we therefore obtained the Taylor-expansion of order
of function
